Spectral Adversary

An attacking or blocking creature that phases out is removed from combat.

Permanents that are phased out are treated as though they don't exist. They can't be the target of spells or abilities, their static abilities have no effect on the game, their triggered abilities can't trigger, they can't attack or block, and so on.

Choices made for permanents as they entered the battlefield are remembered when they phase in.

Phasing out doesn't cause any "leaves the battlefield" abilities to trigger. Similarly, phasing in won't cause any "enters the battlefield" abilities to trigger.

As a permanent phases out, Auras and Equipment attached to it also phase out at the same time. Those Auras and Equipment will phase in at the same time that permanent does, and they'll phase in still attached to that permanent.

After you pay the {1}{U} cost one or more times, a second ability triggers and you choose the targets for it. Players may respond to the new ability at that point. As that ability resolves, Spectral Adversary gets its +1/+1 counters and the target permanents phase out.