The monster doesn't have armor - it has blubber.
Bullets don't bounce of the monster - instead they penetrate, but not deep enough to pass through the protective layer of blubber. The blubber isolates the bullets and then spits thenthem out over time.
But the monster is allergic to this special wood. Instead of expelling the wood shards, the wounds close behind the shard, pushing it deeper until it reaches the vital organs inside, piercing and killing the monster.