The Celestial Gateekeeper token dies, triggering itself, exiling itself and returning
Celestial Gatekeeper from your graveyard to the battlefield.
Celestial Gatekeeper enters the battlefield, triggering
Dual Nature's first ability, creating a token copy of
Celestial Gatekeeper.
Resolve the nontoken Celestial Gateekeeper's trigger, failing to exile itself and returning up to two more Birds and/or Clerics from your graveyard to the battlefield.
If you returned a creature this way,
Dual Nature's first ability triggers, creating a token copy of that creature.
Repeat from step 3.
Resolve all triggers from
Dual Nature's second ability, exiling all tokens with the same name as a creature card that left the battlefield during this combo.