Argentum Masticore

First strike, protection from multicolored
At the beginning of your upkeep, sacrifice this creature unless you discard a card. When you discard a card this way, destroy target nonland permanent an opponent controls with mana value less than or equal to the mana value of the discarded card.

Phyrexia: All Will Be One

First strike, protection from multicolored
At the beginning of your upkeep, sacrifice Argentum Masticore unless you discard a card. When you discard a card this way, destroy target nonland permanent an opponent controls with mana value less than or equal to the mana value of the discarded card.

Phyrexia: All Will Be One Promos

Notably, this means that you may discard a card to keep Argentum Masticore on the battlefield even if there isn't a legal target for that second triggered ability. In that case, no players may respond to the second triggered ability and it does not resolve.

You don't choose a target for Argentum Masticore's upkeep triggered ability at the time it triggers. Rather, a second "reflexive" ability triggers when you discard a card this way. You choose a target for that ability as it goes on the stack. Each player may respond to this triggered ability as normal.