Balloon nightmares. Batman and Robin take turns. Just watch it.
I considered switching to red weapon for Batman, since Red 5 has a very strong charged attack (240 per attack, same damage as charged Red 7) but the Joker spends too much time at the edges of the screen, so it isn't worth it. Too many projectiles will miss and the charge is gone pretty soon after the fight starts anyway. Went with Green 6 instead.
Curiously it's better to charge up Batman with the lower level weapon Green 6 instead of Robin with Green 7 for the boss.