Story Related and unmissable.
Shoot world is the game's fourth world. To get there, you'll need to complete:
Cave World (4 levels, a shop, and a boss)
Fish World (4 levels, a shop, then a 5th level)
Robot World (4 levels, a shop, and a boss)
Levels in Shoot World are mostly vertical and your goal in each 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.
After the fourth level, be sure to refill hearts at the shop.
The Snake boss is more of a chase and I usually had framrate issues here. The goal is to drop all the way 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.
Once you exit the boss level, this achievement will unlock.