Adarkar Valkyrie by tapping it, targeting any legendary creature you control.
Cast
Vesuvan Doppelganger by paying ({3} magic symbol) ({U} magic symbol) ({U} magic symbol) , choosing to have it enter the battlefield as a copy of the legendary creature targeted in step 1.
Put the legendary creature into your graveyard due to the legend rule.
Adarkar Valkyrie and
Intruder Alarm trigger.
Resolve the
Intruder Alarm trigger, untapping all creatures.
Holding priority, activate
Adarkar Valkyrie by tapping it, targeting
Vesuvan Doppelganger.
Resolve the
Adarkar Valkyrie trigger from step 4, returning the legendary creature to the battlefield from your graveyard.
Put
Vesuvan Doppelganger into your graveyard due to the legend rule.
Adarkar Valkyrie and
Intruder Alarm trigger.
Resolve the
Intruder Alarm trigger, untapping all creatures.
Holding priority, activate
Adarkar Valkyrie by tapping it, targeting the legendary creature.
Resolve the
Adarkar Valkyrie trigger from step 9, returning
Vesuvan Doppelganger to the battlefield from your graveyard as a copy of the legendary creature.