OK, professional bouncer advice here.
First, retreat if at all possible. Don’t turn your back and run, but move away as quickly as possible and let the staff know about the problem. If he’s very drunk, as stated, you’re likely to be more nimble and balanced than he is. Keep moving and don’t let him close in on you.
If he’s very close, push/shove him away or off to one side while yelling for help from the staff. The police are, at best, several minutes away. That’s more than enough time to take a serious beat-down. If he’s able to close in on you, grab him in a bear hug pinning his arms and/or tackle him to the floor. Again, shout for help. If the staff can’t/won’t help, often other patrons will when seeing one person being attacked for no reason.
If you have any confidence in your punching skills, a quick jab to the nose can be extremely effective at buying you some maneuvering room but won’t generally end a fight. Unless you’re practiced in kicking moving targets, don’t try the classic “kick in the balls”. It’s harder than most people realize and you’ll be making yourself unbalanced and more vulnerable when you try. Especially on a potentially wet or slippery barroom floor.
Don’t hit someone preemptively with an object like a bottle or such unless you’re looking for a felony assault charge. Even if he swings his fists first, it can still be considered as an escalation, so unless you’re in fear for your life, don’t make any obviously potentially deadly counter moves.
If you get knocked down, go fetal and cover up your head and vitals. Odds are you may get kicked but not stomped. Stomping is a lot worse. Again, keep yelling for help. Don’t worry about appearing like a wimp, just scream bloody murder. You’re not a fighter, so don’t worry about appearances.
If you are honestly in fear for your life, grab a bottle or mug and crack him horizontally above the ear. This will impart maximum acceleration to the skull and thus giving greater chance for a knock out or stun without doing the extensive damage to the bone and brain that a vertical blow to the top of the skull can cause. Generally. Once you decide to strike, anything is possible. Including killing someone with a simple punch to the jaw and depending to the legal climate, self-defense may not be a viable legal defense.