Fiendish Panda's first ability triggers just once for each life-gaining event, whether it's 1 life from Dazzling Angel or 4 life from Apothecary Stomper.

If Fiendish Panda is dealt lethal damage at the same time that you gain life, it won't receive a counter from its first ability in time to save it.

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, Fiendish Panda's first ability will trigger twice. 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.

If you gain an amount of life "for each" of something or "equal to the number" of something, that life is gained as one event and Fiendish Panda's first ability triggers only once.

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

Use Fiendish Panda's power as it last existed on the battlefield to determine which creature cards may be targeted with its last ability. (Feel free to think of this as a metric of just how fiendish the panda was.)