If the target creature is an illegal target by the time Aerial Assault tries to resolve, the spell doesn't resolve. You won't gain life. If the target is legal but is not destroyed (most likely because it has indestructible), you will gain life.

Any abilities that trigger as the target creature is destroyed won't resolve until after you've gained life.

If any creatures were exiled "until" the target creature left the battlefield, those creatures will return before you gain life.