Exemplar of Light's second ability triggers just once for each life-gaining event, whether it's 1 life from Dazzling Angel or 4 life from Apothecary Stomper.

If Exemplar of Light is dealt lethal damage at the same time that you gain life, it won't receive a counter from its second 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, Exemplar of Light's second 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 Exemplar of Light's second ability triggers only once.

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

Exemplar of Light's last ability triggers whenever you put one or more +1/+1 counters on it for any reason, not just as a result of its second ability.