As JGlass so informally pointed out, his teleportation isn't instant, it's works like Goku's IT, or roughly translated, it's going to be a bitch for him to use in a pinch. And against a pissed off Horntail he's going to be doing his damnedest not to be eaten or fried.
"Hmmm, I want to go over there."
Pushes button.
Its not instantaneous, but its quick. Roughly as fast as your brain sending a signal to your finger to push a button. Thats pretty fast. He sees danger coming (not like the dragon will sneak up on him) and he gets to where he needs to be. Simple to understand really.
It's been pointed out that he can't just spam his teleportation technique. How exactly can he beat it if the majority of his weapons won't work?
Once again, tell me why his weapons wont work? Dodging the question doesnt make it go away. Many weapons in the hands of a skilled mercenary attacking the weakest points of a target is very effective.
How's he going to, say, get to the Horntail's underside if the dragon has him cornered on the defense? I doubt he can pull out a weapon from his bag with enough fire power to get the job done without prep time.
How is he gonna corner him again? A giant, ferocious monster doesnt sneak up on you like that. Deadpool will see\hear him coming and run like hell to a better spot to fight from, or bodyslide to a safer place. Hell, idk- like to within striking distance of a weak point of the dragon.
Also what prep time does he need, really? He reaches in and pulls out a weapon. Hes not trying to make a sandwich or take a test at school. He pulls out an explosive device or gun and uses it. No prep time needed.
Deadpool wouldnt be able to use the technique faster than the dragon can breathe flames. He'd be barbecued.
Fixed that for ya. So you mean to tell me he is going to just stand there and watch the dragon shoot fire at him? The dragon doesnt shoot fire at the speed of light or anywhere close to as fast as you are making it seem. Its not so fast that no-one sees it coming or has ever gotten away from the blast. Its happened alot, and with the speed\agility of Deadpool being top notch- he would react accordingly. Your stating these things like he is standing 2 feet from him and not moving. Thats not the case.
If there is any distance at all between them, he will have plenty of time to push a button or react. If this match started and the first thing the dragon did was flap his wings, hover over closer to Deadpool and shoot fire- what makes you think Wade wont move by any means necessary? Its as easy as pushing a button.
And the dragon doesn't need both to see him
No, but if he has one eye he wont be able to see a much smaller opponent when his only good eye is on the opposite side of his head.
Dragons act on instinct. I doubt brain damage would stop a dragon on a rampage.
The dragons reflex ability would cause him to rear back or shake his head from the damage received. His hunting instinct has nothing to do with him reacting to receiving damage. It would cause him to rage, and when you rage you lose focus. Instinct is a complex ability burned into brain function- A natural ability or pattern of action. If his brain is jacked up, his brain function suffers. That means loss of motor function, ability to process smells\sight, etc. Brain damage\trauma screws you up no matter if you are animal or human.
Or the dragon could just stay on the ground, spam fire breath until Deadpool's surrounding melt and he dies in a pool of lava.
Or while he is burning things to the ground, Deadpool would be gone before the smoke cleared and the dragon wouldnt realize until it was too late. Fire brings smoke, dragons cant see through smoke. If Wade gets out of the way, he will be in striking position before the Dragon sees he is gone. He teleports to that big horn hanging over his eye and pumps a few dozen rounds in his eye socket. Damage done. The dragon is now hurt and swiping\biting wildly. He is distracted and off balance thus giving Wade a chance to attack again...
Now to add something to what JGlass said:
Yes Wade can be a coward, but if he is fighting for something- he is pretty good at getting the job done.
This is a tournament. The winners of tournaments get prizes and money. Deadpool likes prizes and money. Plus, if there are no prizes there is still bragging rights to being the winner. Deadpool loves to brag and would want to win to be considered the best.