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Golden Guardian says:

(2): Golden Guardian fights another target creature you control. When
Golden Guardian dies this turn, return it to the Battlefield
transformed under your control

If an opponent targets Guardian with a kill spell, and you activate it's ability in response; it will return transformed. That's great.

But if you activate it's ability to fight another creature, THEN in response your opponent kill-spells it. Does the ability fizzle or will it still revolse returning the Gaudrian to the battlefield transformed?

Golden Guardian will stay dead.

That part of Golden Guardian's ability is a delayed triggered ability. It won't trigger because it's only created during the resolution of the activated ability.

603.7a Delayed triggered abilities are created during the resolution of spells or abilities, as the result of a replacement effect being applied, or as a result of a static ability that allows a player to take an action. A delayed triggered ability won’t trigger until it has actually been created, even if its trigger event occurred just beforehand. Other events that happen earlier may make the trigger event impossible.

Example: Part of an effect reads “When this creature leaves the battlefield,” but the creature in question leaves the battlefield before the spell or ability creating the effect resolves. In this case, the delayed ability never triggers.

Example: If an effect reads “When this creature becomes untapped” and the named creature becomes untapped before the effect resolves, the ability waits for the next time that creature untaps.

(Empahsis mine)

A ruling on Golden Guardian confirms this.

If Golden Guardian leaves the battlefield before its activated ability has resolved, it won’t be returned to the battlefield when the ability resolves.

When Golden Guardian's activated ability resolves,

1. You are instructed to have the Golden Guardian fights another target creature. Nothing happens because the Golden Guardian no longer exists.^{[CR 701.12b]}




2. You are instructed to create a delayed triggered ability. It will never trigger because the creature it references in its trigger condition no longer exists.^{[CR 201.4, 400.7]}

PS - It doesn't fizzle, which means removed from the stack as it would resolve for complete lack of legal targets. It simply doesn't get placed on the stack because it doesn't even trigger.

Golden Guardian will stay dead.

Since the ability doesn't resolve until after Golden Guardian dies, it won't "see" the Guardian die, and therefore won't trigger.

There is a Gatherer ruling that states this specifically:

If Golden Guardian leaves the battlefield before its activated ability has resolved, it won’t be returned to the battlefield when the ability resolves.

If the Golden Guardian dies before its ability resolves, then the ability will effectively do nothing and the Guardian will stay dead.

The ability does two things: it has Golden Guardian fight the target creature, then it creates a delayed triggered ability that brings the Guardian back from the graveyard transformed when it dies. If the Guardian is already dead, the fight instruction will do nothing because both creatures need to be alive to fight, and the triggered ability will be created but it will never trigger because the Guardian is already dead.