I appreciate the hard work that people put into videos of this kind of thing, but some people just want to know where to go. Also, some videos are not in chronological order. This guide will tell you when and where to get each item needed to complete this achievement.
Since there are no maps for blueprints, there are really no official numbers. I've made up my own numbering method to make it easier keep track. I will use K for K-9, S for SP-DR, A for AP-3 and F for FL1-R. For example K1.1 means the first K-9 frame part of that frame and the other three will follow with K1.2 – K1.4, this should make it possible to see at a glance how many pieces of a certain frame you should have. The game does not always keep all of the same named frame parts next to each other. Of course, when you get a whole frame at once, the decimals are not needed.
The Definitive Edition update added map markers for chests, but you still need to know what is in them. It also changed the achievement. You now need 336 blueprints regardless of the source.
You can get your first blueprint on the way into Pylon 512. Boost, jump and boost again to get to a chest holding the White Bare Bones K-9 Head (K1.1). The next one continues the set with the White Bare Bones K-9 Hindlegs (K1.2). You'll find it in the room just after you pass through the Ringers in Pylon 512, on the opposite side of the column from the Cell Bot. The next one is in the room above the core, it won't open until you powered the switch and extracted the core. It contains the White Salty Dog K-9 Forelegs (K2.1). In the room with the furnace looking thing, the switch will open a door across the way that you can get to with dashing and jumping. You will find the White Bare Bones K-9 Augment (K1.3) there. In the next room, head up the ramp to your left to get the White Salty Dog K-9 Augment (K2.2). The chest in the next room, just past the broken wall, contains the entire White Wild Child K-9 (K3) set. When you exit Pylon 512, turn around and jump up to a platform right above the exit to find the White Stinger FL1-R Weapon (F1.1). South of that, not too far from the door that you entered the Lonely Basin from, is a chest on a high rock that has the White Stinger FL1-R Head (F1.2). While you are in the area, go ahead and enter the Brood Hive. Most of the chests in there are crafting items, but there are a few that I will list here. Across the big room, past the door opened by the green switch that is not the main exit, you will find White Iron Tusk SP-DR Weapons Array (S1.1) and if you complete all of the objectives you will get the rest of it at the end of the dungeon (S1.2 – S1.4). Back in the Pylon 512 area, head on top of the building and just east of the glowing pyramid is a chest with the Yellow Bare Bones K-9 Hindlegs (K4.1). There is a chest inside a small building nearby, not too far from where the cables connect to the ground. It contains the White Brute Legs (A1.1). On the rocks nearby, a chest initiates a battle and it contains Yellow Bare Bones K-9 Forelegs (K4.2). Heading back toward Pylon 512, a series of platforms sits on top of a rounded structure. Inside the south side a chest contains Yellow Bare Bones K-9 Augment (K4.3). Look south of the Pylon 512 structure and follow the trail of black maetal to a small cliff with White Brute Augment (A1.2). Now go north of the Pylon 512 fast travel point. Follow the cliffs to the right and then look up a litte on your left to find the chest with White Brute Torso (A1.3). Heading toward the next goal, you will see a wall with blue crystals. Turn around and see the chest in a little rock inlet with Yellow Bare Bones K-9 Head (K4.4). You may have destroyed 5 enemies with Macks's Lethal by now and have the Blue Salty Dog K-9 (K5) set. While you are looking around the area near the gate, you'll see this one in a cave on the ground nearby, it contains White Salty Dog K-9 Hindlegs (K2.3). Inside Cavern Rush, you will get the Green Bare Bones K-9 (K6) set if you can meet all of the goals. Past the newly opened gate, drop down the cliff a bit near the fast travel station to find a chest (the one you may have seen from the ground earlier) with White Salty Dog K-9 Head (K2.4).
At the beginning of The Cradle, come around the cliff past all the high platforms once you have dropped down to find a chest in a cave with Yellow Wild Child Augment (K7.1). When you first get to the tunnels around the pit, go into the short one to the right first to find a chest with Yellow Wild Child K-9 Head (K7.2). Partway up the tower rescuing the Cell Bots, a chest holds Red Wild Child Augment (K8.1). On top of the partly buried ship in the quicksand is a chest with Red Wild Child K-9 Head (K8.2). Out in the middle of rhe quicksand, on a platform you need to carefully boost jump to, is a chest with Yellow Iron Tusk SP-DR Body (S2.1). Once you cross the bubble platforms, the next tunnel has Red Wild Child K-9 Forelegs (K8.3) just past the hole in the side.
Once you get Seth, you'll want to go back to the Granite Steps and get the chest on the rocks with the tracks near your crawler that contains the entire Blue Widowmaker SP-DR (S3) set. Back in the Lonely Basin, climb the big tall rock next to the yellow metal platforms to find a chest with White Stinger FL1-R Jets (F1.3). From there, you can see a chest on the yellow platforms that has White Stinger FL1-R Augment (F1.4). Back in Pylon 512, there is a place where you can ump from the bridge near the center of the big room to a set of big steps. Jump from there and attach to the center track to take you over to another track that leads to a chest with White Bare Bones K-9 Forelegs (K1.4). Back in the Brood Hive, you should have no trouble getting the combo multiplier to x15 for the White Widowmaker SP-DR (S4) set. Near the gate to The Cradle, there is a chest on a rock that requires you to jump over from a rock accessed by a track. The chest contains the entire Red Iron Tusk SP-DR (S5) set. In the rusty area, look up toward a pipe on the wall. There is a chest near there, on a platform needing some fancy jumping, containing White Hatchling SP-DR Legs (S6.1). Inside the enclosure where Repository Blitz is located there is a chest with White Hatchling SP-DR Augment (S6.2). For getting all of the goals in Repository Blitz, you will get the Red Orek-A10 AP-3 (A2) set. On top of the tallest tower, just outside the walls of the Repository Blitz area, a chest holds White Hatchling SP-DR Weapons Array (S6.3). Take the ringers and the track to a previously inaccessible rock out in the middle of the desert and the chest contains White Hatchling SP-DR Body (S6.4).
Now go back to The Cradle and head down the path near Kai's Crawler. The enemy here is low 20s, but you can take him pretty easily. A battle chest at the end of the path contains the entire Red Hatchling SP-DR (S7) set. Go climb the big square building. Drop off the left to find the Blue Iron Tusk SP-DR Body (S8.1) and Blue Iron Tusk SP-DR Legs (S8.2). Climb back up and drop off the right side to find the Blue Iron Tusk SP-DR Weapons Array (S8.3) and Blue Iron Tusk SP-DR Augment (S8.4). Head toward the gate leading out of this area, locked now, and open a battle chest containing White Orek-A10 AP-3 Augment (A3.1) and White Orek-A10 AP-3 Head (A3.2). Now let's go toward the Foundry. On the cliff you get to after the first sets of tracks on the buildings is a chest with Red Wild Child K-9 Hindlegs (K8.4). Once you reach the drill platform outside of the Foundry, go around the back next to a green rock. The chest there contains the White Orek-A10 AP-3 Torso (A3.3) and White Orek-A10 AP-3 Legs (A3.4). You may have killed a lot of red K-9 bots by now and received the Red Salty Dog K-9 (K9) set. If you want to, travel to the quicksand area with all of the tracks and go to the Assembly. You get the Purple Widowmaker SP-DR (S9) set there. It's also a good place to destroy bots with yellow lethals for the Yellow Hatchling SP-DR (S10) set. Outside, you can get up to a chest by jumping up the rocks and then from some platforms to a stack of boxes and then over to where the chest is. It contains Yellow Iron Tusk SP-DR Weapons Array (S2.2). Go ride the rails over to a platform and a chest there contains Yellow Wild Child K-9 Forelegs (K7.3). Behind you, and past two ringers, is a chest with Yellow Iron Tusk SP-DR Legs (S2.3).
In the Foundry, the room after the first Corebot battle has a couple of bubble platforms that will get you over to a chest with Blue Hatchling SP-DR Legs (S11.1). Above the hallway of rollers, you will find the Blue Hatchling SP-DR Weapons Array (S11.2). On the other side of the series of track rollers, behind you just before the forcefield area, is a chest you can jump up to that contains Blue Hatchling SP-DR Body (S11.3). Now that you have all three colors, I suggest you go to the Crucible. You'll get the White Fugu FL1-R (F2) set for a successful all goals run. In the Shifting Sands again, straight ahead of the fast travel point is a tunnel leading to a dungeon you can't complete yet. Just past that, on a ledge over the edge, is a chest with Green Orek-A10 AP-3 Head (A4.1) and Green Orek-A10 AP-3 Augment A4.2).On the way to the goal, after you find the rocks blocking the gate, there is a four sided platform. On one of the sides is a chest with the Yellow Salty Dog K-9 (K10) set. The area just west of the main entrance to the Lonely Basin has a rock for Duncan to break in it, a chest there holds White Brute Head (A1.4). By now, you have probably completed or are pretty close to destroying 10 blue K-9s for the Blue Bare Bones K-9 (K11) set and destroying 10 red SP-DRs and instantly extracting 5 SP-DRs for the Red Widowmaker SP-DR (S12) and Yellow Widowmaker SP-DR (S13) sets. Go back to the Foundry and in the room with the console that summons the track, then use Duncan to flip a big switch on the platform the track first takes you to. The center one of the three chests inside contains Blue Hatchling SP-DR Augment (S11.4).
Now go break down that rock barrier to get access to the rest of the Shifting Sands. As you pass through the area ahead, look to the left for a chest with Yellow Orek-A10 AP-3 Head (A5.1) and Yellow Orek-A10 AP-3 Augment (A5.2). As you emerge, keep to the left and climb a bit past three parts to get a chest with Yellow Orek-A10 AP-3 Torso (A5.3) and Yellow Orek-A10 AP-3 Legs (A5.4). Hop down and follow the rocks around to a chest with the entire Purple Orek-A10 AP-3 (A6) set. Nearby, you will see a bunch of pipes. You can use Duncan to knock one down to get up to the chest on top of a nearby one that contains the entire Yellow Brute AP-3 (A7) set. There is a fast travel station nearby and on top of the arch near there is a chest with the Blue Wild Child K-9 Head (K12.1) and Blue Wild Child K-9 Augment (K12.2). Go back down to the travel point and hug the rocks as you go around to the other side to avoid high level fights. The chest here has the entire Orange Stinger FL1-R (F3) set. You'll find the Forsaken Halls dungeon on your way south, three of the Cellbots are easy enough but the fourth one is on a rock past some high level enemies. You will actually get two sets of blueprints here for a totally successful run, the Red Brute AP-3 (A8) and the Orange Widowmaker SP-DR (S14). Your next destination is the huge hand, on top of it you will find a chest with the entire Purple Iron Tusk SP-DR (S15) set. Head over to where the hand points and enter a indentation in the rocks where you will find a chest with Green Orek-A10 AP-3 Torso (A4.3) and Green Orek-A10 AP-3 Legs (A4.4). Past the hand the other way is a fast travel point under an arch, climb up the rocks nearby and come around the other side to find a chest with the entire Blue Fugu FL1-R (F4) set. Now climb up and over the arch to find a chest with the entire Green Salty Dog K-9 (K13) set on the way down the other side. Partway up to the Coliseum dungen is a chest with the entire Orange Orek-A10 AP-3 (A9) set. Now climb around the other direction and jump across a small gap to find a chest with the entire Purple Fugu FL1-R (F5) set. Head all the way south and climb the rocks there to find a chest with Blue Wild Child K-9 Forelegs (K12.3) and Blue Wild Child K-9 Hindlegs (K12.4). Follow the rocks a bit farther west to find a chest in a small crevasse that contains the entire Orange Fugu FL1-R (F6) set. Now climb the rocks past the Coliseum entrance toward a blue flag to find the entire Green Stinger FL1-R (F7) set. Now I suggest you fast travel, rather than walk, to the north travel point. Stay on the north rocks to avoid enemies. In a low spot, there is a chest with the entire Green Wild Child K-9 (K14) set. As you continue, do your best to avoid the attentions of a high level FL1-R wandering around. The next chest has the entire Green Iron Tusk SP-DR (S16) set. In the area above the Obsidian Run dungeon, follow the rocks around to find a chest with the entire Purple Wild Child K-9 (K15) set. Keep going past the broken bridges leading to Acid Marsh to find a chest with the entire Orange Iron Tusk SP-DR (S17) set. Just outside the entrance to Acid Marsh is a chest with the entire Red Fugu FL1-R (F8) set. Go ahead and go inside, you'll get two sets for total completion: Orange Kraken FLR-1 (F9) and Orange Salty Dog K-9 (K16). In the Obsidian Run, you will also get two sets if you complete all of the goals: Yellow Kraken FL1-R (F10) and Purple Brute AP-3 (A10). On the way to the Warren, go around a big rock not too far from where the Warren is to find a chest with the entire Yellow Fugu FL1-R (F11) set. Once you get across to the other side of the tracks, go past the entrance to the Warren to find a chest with the entire Blue Orek-A10 AP-3 (A11) set. There are a lot of chests in the Warren, but they are just crafting items or quest required.
Now that we have the FL1-R, it's time to go wrap up the loose ends. Head back to the crawler and toward the exit gate to the Lonely Basin from the Granite Steps. Use the vent to get up to the rocks across from the Tyrant's Forge and then do a running dash-jump-jump-dash to get to the rocks with the chest that contains the entire Blue Kraken FL1-R (F12) set. In the northeast Lonely Basin, not too far from the Proving Grounds, a chest sits out in the open. Take out the defenders to get the Blue Stinger FL1-R Weapon (F13.1), the rest of the set is a reward for completing the key and switches goals in the Proving Grounds dungeon (F13.2 – F13.4). Head to the south travel point in the Cradle and ride the steam over to the building and open the chest there for Yellow Wild Child K-9 Hindlegs (K7.4). Over by the quicksand with all of the tracks go up all of the rails and when you get to the tower after the two ringers use the FL1-R to float toward a platform with a chest to get the Yellow Iron Tusk SP-DR Augment (S2.4).Enter the House of Steel dungeon to get the Orange Wild Child K-9 (K17) set for full completion. Completing Armory Flux will get you the Yellow Hammer Fist AP-3 (A12) set. The Coliseum gets you two sets if you meet all of the goals: Orange Hatchling SP-DR (S18) and Purple Hammer Fist AP-3 (A13). The Pit of Oblivion will net you the Green Fugu FL1-R (F14) set if you get all goals. Lastly, completing the Tyrant's Forge gets you both the Orange Hammer Fist AP-3 (A14) set and a full K-9 AOK Chrome set that is just cool to look at.
You should also have the following frames for completing the rest of the goals the K-9 and SP-DR frames: Destroy 10 red and 10 blue K-9s = Purple Salty Dog set (K18), Instant extract 10 K-9s = Orange Bare Bones K-9 set (K19), Destroy 5 purple K-9 with K-9 = Purple Bare Bones K-9 set (K20), Destroy 10 blue and 10 yellow SP-DRs = Green Hatchling SP-DR (S19), Destroy 10 rare SP-DRs = Green Widowmaker SP-DR set (S20), Destroy 5 purple SP-DR with SP-DR = Purple Hatchling SP-DR set (S21).
I'm not spelling out the goals for the AP-3 and FL1-R since I did not start that list in the paragraphs above. I will just list the frames you will have when you complete all of the goals. White Hammer Fist AP-3 set (A15), Blue Brute AP-3 (A16), Red Hammer Fist AP-3 (A17), Blue Hammer Fist AP-3 (A18), Green Brute AP-3 (A19), Orange Brute AP-3 (A20), Green Hammer Fist AP-3 (A21), White Kraken FL1-R (F15), Red Kraken FL1-R (F16), Yellow Stinger FL1-R (F17), Red Stinger FL1-R (F18), Purple Kraken FL1-R (F19), Green Kraken FL1-R (F20), Purple Stinger FL1-R (F21).
The new content that was added with Definitive Edition will help those of us who are a bit too slow to get all of the dungeon blueprints get to the required number.