I just want to add that the description for this achievement is misleading:
you do not need "destroy" the enemy with a web-strike, JUST HIS ARMOR.A more accurate description would be:
Destroyed any armored enemy's ARMOR using a web-strike.For this you need to have defeated Kraven and received the ionic web ability (
)
With a fully upgraded ionic web, you just need to shoot 2-3 web shots, and then hit RB on an armored enemy. You should hear a sound similar to glass breaking, and then the achievement will pop.
If you do not have the ionic web fully upgraded, you may need to fire a few more to get the armor to start disintegrating.
Questions, corrections and neg vote justifications below.