If multiple creatures and/or planeswalkers you control die at the same time, the first ability of Ajani’s Last Stand triggers that many times. However, you can sacrifice it only once, so you’ll get only one token.

In a Magic game, cards are discarded only from a player’s hand. Effects that put cards from a player’s library into that player’s graveyard do not cause those cards to be discarded.

If a spell or ability an opponent controls causes you to make a choice and you choose to discard Ajani’s Last Stand, its last ability will trigger.