Bair is too good. Get him cornered and space bairs to knock him offstage, even at low%.
Have good edgeguards. Put out a hitbox to cover side b (nair,bair, run off DJ nair), then go out for the kill when he upBs too close, or just take the ledge.
Fish for knockdowns with running shine, nair shine, drill shine at low%. Learn to thunder combo, or simply tech chase to get your grabs. Chain grab, it's easy and broken. uthrow, utilt, usmash, uair him all across the stage and platforms then hit him off stage with bair at mid/high%.
FH nair is fine, even if it's more effective in the ditto than vs falco.
Platforms are your friends : retreat safely, run off bair, shield drop is OP, bait him to leave the ground to take back some stage or intercept him. When there's no platform , on FD, approaching can get tough, but the CG more than makes up for it. Practice CG vs 20xx bots and erase falco stocks EZ on FD, it's actually your best stage because of this.