This achievement requires completing the game without dying. I used the Brick Head (to prevent breaking up when taking damage) the Scythe, and the Shark Fin up until the shop before the final boss where I swapped to the Shotgun.
Edit: users in the comments have reported that the lightning gun is a better choice than the shotgun.
Along the way you'll need to play through the five worlds and defeat four bosses. After the first and second bosses you drop into an area with Sally. If you have full health, she will increase the max ammo for your weapon and if you don't, she will heal you instead. Get close to her and press
a few times and you will drop your weapon, then your backpack. She will then grant you an additional heart which is lost if you die (but you won't be dying for this achievement). Doing this both times you encounter Sally will result in having 2 extra hearts of health which makes a big difference.
Since you won't be using your glyphs to continue, you'll instead use them at shops to buy hearts, then reroll the vendor stock for more hearts if needed. I found the shotgun to be better against the final boss so I changed to it at the last shop.
Cave World is easy. Be careful to combo enemies and get glyphs. If you kill all the enemies in the third area, a new world snake appears that leads to a secret area with numerous flying enemies and several glyphs. The fourth area often contains a slim upward path to a room with four glyphs.
The three bat boss is pretty trivial with the Scythe and Shark Fin. When the screen loads, wait for the three of them to be close together near the top of the screen, then drop in and you can kill them with one Shark Fin barrage.
Fish World was apparently added with an update and not part of the original PC game. There's not much going on in these four areas nor is there a boss after the shop. You can try to combo the enemies if you need glyphs or you can just run along the bottom of each area where there are no enemies and climb up the final wall to the exit.
The shop seems to randomly have 2-5 glyphs on platforms that can be gotten to by jumping on balloons.
The final area is simply an ascent to the exit at the top and if you go to the far right wall, you can almost always climb up to the top unimpeded. After exiting you'll drop into an area with a tree to the right full of hearts and ammo.
Robot World has several new enemies that can be annoying as well as gaps that, if fallen into, kill you. You shouldn't need to build glyphs here so your goal is to safely and quickly get to the exit. The first two areas are generally short and the third and forth are usually longer. Try to get height and bounce off of the copter enemies and if you seem to be approaching a clusterfuck, shark fin barrage forward.
The boss is a joke with the Scythe so you shouldn't need to worry about filling up hearts in the shop- as long as you have one or two you should be fine. As soon as you drop into the boss area, run directly right and ignore (run under) the copter enemies if you can. Turrets will be shooting at you but as long as you keep moving forward you should avoid them. As soon as you get to the boss, use a shark fin barrage on the center red panel, then push under the boss and you should destroy his bottom two panels. Then get to the right of him and jump up to attack his upper right panel to kill him.
Be sure to get another health upgrade from Sally. With the Brick Head you'll have five hearts now.
Shooty World is basically vertical and your goal in each area is to get to the exit at the bottom. The most annoying enemies are the rotating turrets. You ideally want to just drop down without engaging anything unless you need to try to refill glyphs. If you'd prefer to carefully fight your way down, that's an option, too. Remember that if you take damage, you'll remain in an immune animation until you touch the ground, so use this to your advantage as you fall downward to the bottom.
You definitely want to fill hearts at the shop since you don't get a free heal from Sally after the boss. Unless I missed something (entirely possible), you need to get from this shop to the shop after the four areas of Death World for another Shop where you can buy hearts again.
The Snake boss is more of a chase and I usually had framrate issues here. The goal is to drop down to the bottom, then head to the right to get to the exit. You'll encounter various normal enemies along the way and if you don't progress quickly enough, you'll also be attacked by several red snakes which you can fend off by hitting them in the face. You want to keep moving as quickly as possible to stay ahead of the snakes as best you can. Once you get to the bottom and start heading right, a shark fin barrage can give you some speed and/or clear through normal enemies should any be along the path. The snakes can be killed but I found it easier to just rush to the exit.
Sally is not present in the next area so you aren't given a full heal like in previous worlds.
Death World is structured a little differently. Exits will either be in the upper right side or somewhere in the lower central part of each area. There are tons of enemies- be careful with the red tombstones which can be broken with the scythe but beware as the broken stumps will still hurt you. It's up to you how you want to approach these areas, as you can either drop down and then head right, or head right, then drop down. If you get to the lower part of an area and don't find an exit, you'll eventually see the world snake along the right side of the area and you'll need to climb up to him, which can sometimes be a hassle based on how the area is generated.
When you reach the shop, I suggest refilling hearts and buying the shotgun. I had a hard time using the scythe against the final boss and found the shotgun to be much more effective.
EDIT: Several players have reported that other guns are much better than the shotgun. The lightning gun especially.
The area with the final boss is pretty large. The goal is to shoot him in the eyes, and I found it best to move right, kill/avoid normal enemies, and watch out for his lunges. There are generally multiple healing mounds along the way, so getting a few extra hearts in the course of the battle can be key. He is constantly protected by a cluster of blue blobs, some of which will continually turn red and dash at you. They are invulnerable when blue but can be killed when red.
After dealing enough damage to the boss' eyes, he will die and you'll then be taken to the final area. Interact with the skull to end the game, after which this achievement will unlock.