Story Related and Unmissable.
Robot 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 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 (I'm assuming you're using the scythe).
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/jump over) 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.