Flying, vigilance, indestructible
Other permanents you control have indestructible.
A planeswalker with indestructible still loses loyalty as it's dealt damage. It is put into its owner's graveyard if its loyalty becomes 0.
Because damage remains marked on a creature until the damage is removed as the turn ends, nonlethal damage dealt to a creature you control may become lethal if Avacyn leaves the battlefield during that turn.