Each creature with lifelink dealing combat damage causes a separate life-gaining event. For example, if two creatures you control with lifelink deal combat damage at the same time, Enduring Tenacity's first ability will trigger twice and you may choose a different opponent for each trigger. However, if a single creature you control with lifelink deals combat damage to multiple creatures, players, planeswalkers, and/or battles at the same time (perhaps because it has trample or was blocked by more than one creature), the ability will trigger only once.

A token that's a copy of Enduring Tenacity won't return to the battlefield when its last ability resolves.

If a nontoken permanent that's a copy of Enduring Tenacity dies while it's a creature, it will return to the battlefield as an enchantment when its last ability resolves. It won't have any card types other than enchantment.

If you gain an amount of life "for each" of something, that life is gained as one event and Enduring Tenacity's first ability triggers only once.

If an ability triggers whenever an opponent loses life and its effect causes you to gain life, such as the ability of Exquisite Blood, this will loop until either you win the game or a player takes an action to break the loop.

In a Two-Headed Giant game, life gained by your teammate won't cause Enduring Tenacity's first ability to trigger, even though it caused your team's life total to increase.

Snake and Glimmer are both creature types. Enduring Tenacity won't have those creature types when its last ability returns it to the battlefield because it won't be a creature.