Story Related and unmissable.
Death World is the game's final 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)
Shoot World (4 levels, a shop, and a boss)
Death World is structured a little differently then the previous worlds. Exits will either be in the upper right side or somewhere in the lower central part of each level. There are tons of enemies- be careful with the red tombstones which can be destroyed but their 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.
Get through four basic levels to find the shop. After leaving the Death World shop, this achievement will unlock.