I was wondering what the ruling is on improved targeting vs the hand ata.

I'm using iron-man 001 from the Iron-man set, I was wondering if I use improved targeting on let's say hobgoblin prime, and he has the hand ata, and is adjacent to a piece of blocking terrain. Would it activate the hand ata. Since the Iron-man ignores blocking terrain for shooting.

It doesn't matter what Iron Man ignores.
If blocking terrain was blocking the line of fire, then sure, IM shoots through it.

But in this case, the ATA blocks line of fire being drawn to that character if they meet the adjacent-to-blocking requirement.

Correct. Due to the wording of the Hand ATA, what you have is a situation where even though Iron Man ignores blocking terrain for line of fire purposes, the check is for The Hand characters' adjacency to the blocking terrain, which is what blocks the LoF. The fact that he can destroy it afterward doesn't matter for this attack, because they are still adjacent to it until after the attack resolves.