As of the Tidal Basin update, there are three craftable exotic weapons. First and *easiest* is the
Kendra's Liberty. This is really easy if you have already acquired a high end D50 and held onto it, as the parts needed to craft it are guaranteed drops. However, the high end D50 itself is incredibly rare, so if you don't have one already move on to option two. Second is the
Chatterbox. This is the one you should aim for if you don't have the D50. The good news about the Chatterbox is that it doesn't need a specific high end weapon to craft, unfortunately the parts it does need are not guaranteed drops. They do seem to be high percentage drops though. Third is the
Nemesis. The parts for this weapon are guaranteed drops, but they can't be gotten till world tier 5, and require going through a 3 week cycle.
Kendra's Liberty: It is
CRITICAL that you do this in order. If you do, the parts should drop no problem.
First-Beat the
Capitol Building Stronghold and a mid-mission boss will drop the
Pistol Trigger and Mechanism.
Second-Beat the
American History Museum and the end boss will drop the
Receiver and Paint-job.
Third-Beat the
ViewPoint Museum and the end boss will drop the
Pistol Sight and Rail.
Fourth-Beat the
Space Administration HQ and the end boss will drop the
Pistol Grip and Tags as well as the blueprint for crafting the weapon.
These missions can be done on story/normal difficulty, the parts will drop so long as you do them in the right order.
Chatterbox: The parts for this weapon drop from Hyena caches but aren't guaranteed. You must open the caches in a specific section of DC for a chance at the parts. The order you go after the three parts in shouldn't matter, but the blueprint can not be gotten until you have all the parts, so that step must be done last. You need one Hyena key to open each cache and those can be gotten by looting wall boxes in any underground area. You will get a random key from the wall box regardless of where you are searching, so there is a 25% chance it will be a Hyena key. There are usually multiple boxes per underground area. When you have at least 4 keys (more to be safe as the drops aren't guaranteed) you can begin.
First-Open a Hyena Cache in
Downtown East and it may drop the
Loaded Canister. There are two caches in the Grand Washington Hotel mission. The first is in a bathroom under a sink (this part is after the lobby part) and the second is to the right immediately after getting to the rooftop.
Second-Open a Hyena Cache in
Federal Triangle and it may drop the
Creative Mag. You can find a cache in the Jefferson Trade Center mission, in the loading dock to the right before leaving the garage. Another in freeplay, go to a building northeast of the safe house with an open courtyard in the middle and climb a ladder onto some scaffolding.
Third-Open a Hyena Cache in
Judiciary Square and it may drop the
Modified Mods. One cache can be found in the police station on Indiana Avenue just past The Cinderblock Control Point. Head inside and go down to the car area and the cache is located by a machine gun nest.
Fourth-Replay the
Bank Headquarters mission, difficulty doesn't matter. Play until you get to the room with the giant window and the computers. When you enter, immediately to the left there will be a wall with an off colored plank. You can now press a button on that plank that will open a safe where you can collect a key card. The button will only appear if you have the first three parts. Continue playing until you get to the vault. Once inside, immediately go to he left and you will find a golden gate you can now open with the key card. Inside is a Hyena cache that will drop the
Lost Chatterbox Blueprint. If for some reason the blueprint isn't dropping and you have all the parts, try advancing to the final world tier and trying again.
A couple of additional notes on the Chatterbox. You don't need to go to the Hyena caches I pointed out. You can look up or discover your own, as long as it is in the section of the city I pointed out (video below for more locations). If the cache doesn't drop the part, either find another cache, or wait 24 hours for the cache to refresh. Also, you do not need to be the one opening the cache. If you are playing with a friend, they can open the box and you each have a shot at getting the drop. For me, I did this with a friend. This allowed us to double up our chances when looking for keys. However, you can't farm the boxes with a friend. If you opened the cache in your world with a friend, then go into your friend's world to open the same cache, both of you will get nothing.
Here are some videos from Zasta 360GameTV containing Hyena cache locations (look in the description, he has the caches divided by city area, so you can check for the area you need) and a bunch of key farming locations:
Caches:
Keys:
For context on the drop rates for the parts, this was my experience:
My friend and I did the GWH mission (I was hosting). I opened the first box and he got the part while I didn't. However, when we got to the second box in the mission, he opened it and I did get the part. For the second part we replayed the JTC mission. He opened the box in that mission but neither of us got the part. We found the box in freeplay that I pointed out, I opened the box and we both got the part. For the third part we went to the box in freeplay that I pointed out, I opened it and we both got the Part. So in total he went 3/4 and I went 3/5. The final step is guaranteed.
Nemesis: The parts for this weapon can not be gotten until you advance to world tier 5. Once you get to world tier 5, every week three missions connected to a stronghold will be invaded. Beat those three missions, and the invaded stronghold will be unlocked. Beat that invaded stronghold and the Tidal Basin stronghold will be unlocked. This repeats every week with a different set of three missions connected to a stronghold. You will need to get the first part from Tidal basin, and the next three parts from the three invaded strongholds. If you have already beaten the weeks invaded missions don't worry. Go to the mission on the map, hold Y to replay and select difficulty. On the select difficulty menu you can hold Y again to toggle the mission or stronghold to invaded. You can only do this for that weeks invaded missions and stronghold though. That means that each week you can only play one of the three strongholds on invaded mode and thus can only get one of the last three parts each week. The blueprint drops from the invaded Grand Washington Hotel mission, but will not drop unless you have all of the parts. This means that if you don't have all the parts when that mission becomes available, you will have to go through another three week cycle of missions, get the parts you are missing and then go for the blueprint when its available again.
First-Replay the
Tidal Basin Stronghold after reaching world tier 5. Difficulty doesn't matter. Play until you are asked to patch ISAC into a laptop. After interacting with the laptop take the stairs in that room up to the second floor and pick up a key, it should be hard to miss. Continue playing until you board the hover craft. At the end of the first big battle in the hover craft go the the door on the left instead of moving to the outside of the craft via the door on the right. Open the door with the key you acquired before and inside you will find a lootable weapon crate. The crate will contain an Adrestia SR1. Deconstruct this weapon and you will receive the
Marksman Rifle: Scope – The Tally.
Second-Fourth-Replay the three strongholds on invaded mode when they are available and the end boss will drop a part. Difficulty doesn't matter. This was the order for the first three weeks after World Tier 5 launched:
Capital Building-Marksman Rifle: Scope-The Scourge Roosevelt Island-Marksman Rifle: Bolt-The Scales District Union Arena-Marksman Rifle: Stock-The BridleFifth-Replay the
Grand Washington Hotel mission on invaded mode, difficulty doesn't matter. The first named boss, Puck, will drop the blueprint. He appears very early in the mission. This mission is linked to the DUA stronghold and can only be played on invaded mode once every three weeks. The blueprint will not drop unless you have all four parts.
The first part is a grunted drop from deconstructing the weapon. Parts two through four are guaranteed drops as long as you already have the first part. The blueprint is a guaranteed drop as long as you already have all of the parts.
A word of caution. Multiple people have gotten the TB part, then the CB part (the first invaded stronghold at world tier 5's launch) and then joined player's games at lower tiers to play the other two strongholds on invaded mode. This worked for the third part but not the fourth part, and this was the case regardless of which mission they did first. Meaning, after getting the first two parts people have joined lower world tiers and gotten the part from the RI stronghold and then did the DUA stronghold and gotten nothing, while other players have gotten the first two parts, joined a lower tier and got the part from the DUA stronghold, then played the RI stronghold and got nothing. This likely means the intended way to get this exotic is to wait for the missions to cycle over 3 weeks. It may not be a big deal, but with other things in this game, doing things the unintended way could mess up your game. For example, people have killed hunters the unintended way and many of them are, for the time being, locked out of getting all 8 ivory keys. Other players have experienced glitches where a part for the Kendra's Liberty dropped out of order, causing one of the other parts to not drop at all, or the final part they get to not drop with the blueprint. So if the GWH invaded mission becomes available and you're missing a part from the two unavailable strongholds, you could try getting your missing parts by joining lower World Tier players instead of waiting the 3 weeks, but it could completely screw up the rest of the drops. It's your call.
Credit to Bomb 2 chest for pointing out the correct order of missions for the Kendra's Liberty, DoonDoons for confirming that the parts drop on story/normal difficulty and to Fooga for making me aware of the Chatterbox's existence