If your life total is brought to 0 or less at the same time that Sun-Crowned Hunters is dealt damage, you lose the game before its enrage ability resolves.

If lethal damage is dealt to a creature with an enrage ability, that ability triggers. The creature with that enrage ability leaves the battlefield before that ability resolves, so it won’t be affected by the resolving ability.

If multiple sources deal damage to a creature with an enrage ability at the same time, most likely because multiple creatures blocked that creature, the enrage ability triggers only once.