I apologize if this came up before, but my extensive 45 seconds of searching did not yield an answer.

Cluster missiles; if the first attack kills the target, does the attacker get to choose a second target for the second volley?

No.

You've fired at the target and now it is gone so there is nothing more you can do to it.

Consider that if you had a Fire Control System on the same ship as a Weapon's Engineer if you fire one a ship and destroy it the FCS will not trigger which it turn means the WE doesn't get to pick a TL either.

I am kust going off memory but doesnt the card say "this attack"?

I apologize if this came up before, but my extensive 45 seconds of searching did not yield an answer.

Cluster missiles; if the first attack kills the target, does the attacker get to choose a second target for the second volley?

Just for further clarification, here's the FAQ entry on Cluster Missiles.

Cluster Missiles

The attacker only needs to spend one target lock to use Cluster Missiles.

Cluster Missiles is treated as two separate attacks against the same target.

If a ship is equipped with Cluster Missiles and Munitions Failsafe, both attacks must miss for Munitions Failsafe to activate.