I nearly missed the upgrade you could purchase because you need to leave the level select screen so it is very easy to overlook.
I also could not unlock the jetpack because I could not get extra items with the grappling hook. I think I am supposed to use it at the beginning of the third level but Its reach also too limited or I couldn't get the timing right with the double jump.
But overall this is a cool game with some nice peaks of difficulty and replaying with the upgrade feel nice/easier each time