If Kazarov is dealt damage at the same time that a creature an opponent controls is dealt damage, Kazarov must survive the damage to get a +1/+1 counter.
2018-04-27
Kazarov's triggered ability triggers once for each creature dealt damage at one time.
2018-04-27
If a creature is dealt an amount of damage "for each" of something, that damage is dealt as one event and Kazarov's triggered ability triggers only once.
Flying
Whenever a creature an opponent controls is dealt damage, put a +1/+1 counter on Kazarov.
: Kazarov deals 2 damage to target creature.