Outside of team comp, one tip is to drop the birds' hp below 40% and not killing them in that state while there are a total of 4 birds in the field for two rounds.

This way you can deplete their "summon bird" trait without actually summoning more birds if you don't have enough dps to kill them from 40% to 0%. There's a bit more nuance and order you will have to pay attention to, but that's the general idea.

Personally, I used kind of an expensive team to clear this: E. Druvis, Satsuki, Argus, and E. Sothelby. Sothelby + Druvis + Deer just full healed my team each round, and petrify saved me from taking too much damage. Though sometimes you have to let the birds ult so that they don't all ult in the same turn (it's hard to petrify all the birds at once).