Here is a guide on how to use Vader's TIE Advanced to destroy the AT-MP across the gap on Cato Neimoidia The Eastern Arch.
At the beginning of the level you will be faced by an AT-MP across the gap which fires rockets at you.
First destroy the two pillars which can obstruct your throwing path, because if Vader's TIE Advanced even touches one those pillars it will immediately blow up.
It will also immediately blow up if you drop it or get hit by a rocket by the AT-MP while picking it up with the force which is annoying.
After deflecting a few rockets the AT-MP will give you a short break to crunch up Vader's TIE Advanced and throw the crumpled up ship at the AT-MP.
If you succeed in the throw the AT-MP will fall over and blow up (get destroyed).
If you were unsuccessful, you will just have to go and jump off the ledge (commit suicide) to try again.
A quick note is that sometimes the achievement is delayed and might pop after you walk across the extended bridge.
Aside from that good luck and may the force be with you.

Here's a video to help guide you:
http://www.youtube.com/watch?v=Zl4HQYhuNcc