Stock up on speed potions - If you have the cash to buy a supply of the speed+attack coffee from the Twitch Bros shop, do so, but you'll want all the speed potions you can carry. You'll probably have a sufficient supply of PP restoring potions, but they are also fairly useful, so ensure you have plenty.
First important point, get the timing on blocking the global warming presentation correct. The screwed status it inflicts is largely ignorable (This fight will not last 99 turns, one way or another), but the sleep is utterly debilitating.
The secret to beating heavily armored foes who are beyond your ability to defeat normally, I've found, is to control the flow of battle as much as is humanly possible. Unfortunately, being a boss - Al Gore is immune to some of the best statuses to achieve this. So, every turn drink a speed potion to attack twice. Your buddy, however, should probably be feeding you PP restoration items on his turn.
Use your best Defense Down abilities on your first two attacks against Gore. And follow that up with as much damage and DoT as you can - stacking bleed is awesome if you can do it efficiently. Ideally, once he summons his guards he should be almost dead, to the point where the DoT will finish him off in a turn or two so that you can ignore him.
Lastly, block everything! It sounds obvious, but blocking everything can mean the difference between the guards killing you in one round and two rounds. And two rounds means you have an opportunity to heal. Granted, getting the timing right can be tricky sometimes.
Ultimately, what you're wearing and wielding is up to you (Although I recommend at least one of your weapons have an AoE component), but some of the patches/strap-ons are considerably more useful than others.
For weapons (try to avoid any that are already covered by your abilities):
- Ice Damage is one of the best things you have, IMHO, as it applies slow to enemies, giving you more free hits (bosses may be immune to slow, I can't remember).
- Bleed can stack up to 5 times dealing devastating DoT, no matter what their armor is.
- Fire and Gross for additional DoT.
- Have at least one patch that grants PP, go for the one that is likely to be triggered most often.
- The rest are up to you - If you're a fighter, then you may want a +armor patch, because some of your abilities do more damage based on armor, but I honestly find most of the patches lack-luster, providing very little benefit.
I found Butters to be the best for this fight; keep using his basic attack until the guards are summoned and then use Professor Chaos. All of the attacks on Professor Chaos's wheel are powerful, but what I found the most useful was the shield, as it gives some much needed breathing room against these well-armed foes.
Kenny's unicorn summon is another great ability; massive damage and bleed - although my success rate for the QTE is about 75%, and being down an ally for a few turns means all the damage is directed at you.
If they are available to you at this point, Jimmy might be able to temporarily sleep the guards, allowing you to focus on Gore, and deal with one enemy at a time. Stan's in-combat buddy command can lower an opponent's defense while still allowing him to attack.
As I mentioned, controlling the flow of battle is critical when you are outclassed. So if your buddy's health is critical, consider switching them out. If they drink a speed potion, they can attack on the first turn and switch out on the second. And even without a speed potion - it saves you from needing to revive them on the next turn - and the switched in buddy has full HP and PP if they haven't been used yet.