Phase 2's 2nd stage is hella bugged for me. Managed to clear 2-1 though. If it doesn't go through for you on 2-1 you can try refreshing, 9/10 it works and lets me replay a level or play another level without spending stamina.

P.S: Upon further investigation into 2-2, it CAN be solved. It's really strange and you won't encounter any fights... Put all your teams on top and for me at least, the assault pest didn't move. This is good. Turn off auto-move and spam click "Next", stopping and waiting at each encounter. If you encounter the assault pest, it'll freeze on contact with the next encounter.
P.S.S: 2-3 looks good. Haven't tried 2-4 as of now, will get back to you guys.