Ooh, I'm scared. A giant egg! Nothing to worry about, right?? Until she hatches and starts spitting at you!! Mallow and Geno should be able to handle it. Oh, and Mario can come too. Birdo's not especially vulnerable to any one attack, so whatever you want is fine. You probably won't have to attempt the battle more than once or twice.  If you're impatient or afraid of healing items, stay in defence mode once she hatches so her eggs will bounce back at her.