PyroByte, there are instructions and the game actually forces you to go through the screens that tell you how to play every single time you start it. The screen is even labelled "Instructions". I have no idea how you could have missed it.
Crux is just a matter of conserving spew. Just a vertical burst to jump and horizontal burst to throw yourself across the spikes. That should give you enough material to finish the rest of the level. The only other special thing is it'll be easier to bounce across the gap then jump.
Putting in pop ups in the shootable area is the worst idea ever. It's been done in several other Flash games here and every single time it makes the game unplayable.
I demand that they retroactively award this badge! It is an outrage to all of us who have spent, NO INVESTED, so much time and effort into beating this game, to not be award the badge. Think of the arduous journey to the Grinning Colossus, all of the jumping puzzles, and the epic boss fight.....
You want us to repeat all of that just to get the badge?