Solo Character Dungeon Challenge

I challenged my DM to a competition where I'll build my best level 20 character with 10 mythic tiers and I'' go through a ten room dungeon with progressively harder challenges. My question is what type of character is best suited for this type of challenge? He says I'll need combat, skills, and anything else that pathfinder supports. I'd prefer not to go with wizard because it feels cheap.

Inquisitor? Archaeologist Bard? Oracle? Ranger? Do you want no magic? Or just not 9th level arcane casting?

I've just played a ton of wizards recently and know how powerful they can be. I'd like to see if I can beat a dungeon with a slightly more creative build.

Look at the One zen Archer monk guide

Alchemist.
Get your bombs to have a large slew of effects that you can choose from. You'll have good skill options, and powerful buffs (mutagens) if you get stuck in melee.

Any other class that can set up a build like this are also good choices. Magus is therefore not useful (too focused on combat, and with very few support spells), but Inquisitor is a solid choice.

Playing mythic really skews the field. Casting gets even better. You could be a divine caster, or a sorc or other 9 level arcane caster.

Another alternative is playing an undetectable skill monkey.

Have to agree that mythic ranks really blows everything out of the window.

It's easy to make a character that can one-shot about anything as soon as you are allowed a melee attack roll.

For a bit more fun / diversity, I would suggest going for something that usually is a PAIN to level up and play with, but is quite powerful come the late levels : A mystic Theurge. (prestige class)

you pretty much get the full spell-casting ability of both wizard and a cleric, up to 8th level spells. Then you can have fun with that :)
of course, feel free to switch out wizard/cleric for nay combination of arcane/divine spellcaster you want to go with.

you pretty much get the full spell-casting ability of both wizard and a cleric, up to 8th level spells. Then you can have fun with that :)
of course, feel free to switch out wizard/cleric for nay combination of arcane/divine spellcaster you want to go with.

Alternatively, you could have one class with 9th level spells and the other with 7th level spells, if you focus on one of the classes with the non-MT levels more than the other (you could have the effective spell casting levels being 13 and 17 in the two classes).