Yes it's possible to beat the entire game on 00 Agent, enemy rockets

Caverns is the hardest one due to the jack wade radio-in part, it is possible, there's a certain route you gotta go down.
Among the hardest are
-Train
-Silo (probably the second hardest! May actually be just as hard as caverns too upon further recollection)
-and of course caverns!

This is a fun challenge for someone whose already beat the game, I highly recommended it!