It looks like I spoke to soon about always having your hand held as to what to do next, since I spent a merry half an hour stuck. Finally found a route through Sector 2, and killed the eyeball boss thing. Then moved on to Sector 4, which was somewhat simpler to get around. Killed the boss there too – Sector 3 next, it seems.
I have the super jump, ball jump, and power boost now too.