Are hunters invincible ?
No, but they have a ridiculous amount of health and/or armor. I know that I've killed them before by landing a ton of sidewinder shots, but I recently had a run-in with one while using the mighty murderer.. and it just wouldn't die. It ended up killing me even though I had it bugged.
A couple of interesting things to note about hunters. Firstly, if two are coming after you it seems like they'll collide and kill each other much like boulders. I've witnessed this twice. Secondly, they seem to react strangely to the Hunter Hunter item. I was tracking one and he simply wasn't moving at all until I got very close. I also replaced the hunter hunter with a different item in a 1x1 hallway while he was drawing near, and he refused to pass over it. He would charge up to it, stop, and sit there until one of my bullets plinked off of his armor.
Heed my warning: it's very easy to get stuck in the cavern level (the one with the mushrooms and dull brown walls/teal floor). The giant red teethy worm monsters occasionally trigger a caged arena trap, and another will spawn. They react to your bullets by sliding AWAY, however if you're pushing them into one of the walls they can wriggle through them and then you'll have no way to end the trap. You'll be stuck and I haven't been able to find a way to end the game and save my score when I get stuck.
To handle this, carefully pick them off from a safe distance and then move in. If an arena trap triggers, focus your fire as heavily as you can on the large red worm. His death should free you. As long as the bullets are concentrated on him he won't have time to wriggle through the wall.
Killed by the giant yellow "RAARRGHH!!!!" guy. In big open rooms he's just incredibly hard.. unless there's some special way to dodge his stinking bullets.