All first-strike combat damage is dealt at the same time, and, separately, all regular combat damage is dealt at the same time. If one of those amounts of combat damage is enough to cause the player being dealt damage to lose the game, Angel of Destiny's first triggered ability has you gain life, but the other player has already lost the game and can't gain life.

If a creature you control somehow deals combat damage to you (most likely because its combat damage was redirected), you gain twice that much life as a single life-gaining event.

If Angel of Destiny leaves the battlefield before your end step, its last ability won't trigger and won't cause a player to lose the game, even if Angel of Destiny attacked that player earlier.

In a Two-Headed Giant game, Angel of Destiny's last ability can trigger as long as your team's life total is greater than your team's starting life total by 15 or more life.