Best Critical Hit character?

Zero is the only character that really focuses on critical hit damage. Salvador has a few talents to bring it up as well, but doesn't rely on it.
Axton can only skill 5% via ranger, Maya not at all.

So Zero>Salvador>Axton>Maya

Maya's Mind's Eye skill pumps up her critical damage by 5% per point. Combined with phaselock providing a stationary target, she's a very capable sniper

Skill wise i would recommend Zer0 no questions asked. But if your friend really wants to rock a crit based Axton, i would just say use badass points. They are infinite and can give you an infinite amount of upgrades allowing for an infinite chance to upgrade crit damage whenever the opportunity arises. And i only say when the opportunity arises because each upgrade asks you for different choices each time.

Personally I'm focusing on a strong range stronger melee Zer0. For badass points I always try to go for melee damage, crit damage, gun damage, gun accuracy, recoil reduction as a first priority. If none of those come up I also do shield recharge delay, shield recharge rate and max health. In my opinion I think those are the most important. That combo I feel allows for maximum damage and maximum defense. I don't do capacity because what good is a shield if it cant recharge quickly or at all mid fight? A shield that recharges much faster is a better shield than one that is simply higher capacity.

Deffinitly have to agree with everyone here Zeros the way to go im using him myself recently got to the bottom of the sniping skill tree , basicly as long as u keep citical hitting you will increse sniper damge by 5percent and crit damge by 6 this stacks up to 999 times so gets crazy..... Not to mention first perk in that tree increse crit hit damge by 4% per upgrade

The best at critical damage has to be maya because with reaper, mind's eye, and accelerate she becomes a critical hit machine with a good amplify shield. I only use snipers with her. I rarely don't kill with a critical hit.

Maya with minds eye and accelerate, with class mod's providing bonus's to them, and a relic providing more dmg with the gun your using, would be alotta criticals with snipers+headshots i think.