Magic the gathering, ixalan standard, bristling hydra
Your opponent can do this.

After he exerted Ahn-Crop Crasher, the triggered ability went on the stack. Then, you activated Bristling Hydra's activated ability in response, which went on the stack above the triggered ability. Then, your opponent cast Lightning Strike, which went on the stack above your activated ability.

At that point, the stack looks like this (from top to bottom):


Lightning Strike
Bristling Hydra's activated ability
Ahn-Crop Crasher's triggered ability


If no one else does anything, the stack will begin to resolve, starting from the top. So Lightning Strike will resolve. At this point, your Hydra's activated ability has not yet resolve, so the Hydra wouldn't have hexproof yet.