Pyrewild Shaman's last ability triggers only once for each time combat damage is dealt, no matter how many creatures are dealing damage at that time.

Pyrewild Shaman's ability can trigger during each combat damage step. For example, if a creature with first strike deals combat damage, you can return Pyrewild Shaman to your hand, and discard it using its bloodrush ability to pump up an attacking creature without first strike. Then, when that creature deals combat damage, you can return Pyrewild Shaman to your hand again.

Pyrewild Shaman's last ability triggers only if it's in your graveyard when the creatures deal combat damage to a player. It returns only to your hand only if it's still in your graveyard when the ability resolves. Notably, if Pyrewild Shaman is dealt lethal damage at the same time that a creature you control deals combat damage to a player, Pyrewild Shaman's ability won't trigger.

If creatures you control deal combat damage to more than one player at the same time (perhaps because it's a multiplayer game), Pyrewild Shaman's ability will trigger once for each of those players. However, only the first such ability that you pay for will return Pyrewild Shaman to your hand. Even if it returns to your graveyard before the other abilities resolve, it's considered a different Pyrewild Shaman than the one whose ability triggered.