Before following this guide I would recommend playing through Fire Fight first. Playing through Fire Fight will allow you to unlock levels, weapons, arm cannons, and mutators.

Here is what is required for this guide

-Checkpoint (Level)
-Warrior Monk (Mutator)
-Floor is Lava (Mutator)
-Sharpened Steel (Difficulty)

My method for reaching level 80 is to play Checkpoint as many times as you need to level up. Checkpoint is a small map which will help you complete it quickly. The mutators and difficulty will help you to achieve level 80.

Run 1
71,100 - 1:48.87
Run 2
74,400 - 1:25.29
Run 3
67,500 - 1:52.60

I can add a walkthrough video as well.

Leveling up is based on score. Score is accumulated in game but can also be effected by Difficulty and Mutators.

You want to use mutators that have atleast a 1.1 rating.

Mutators:

[1.1+ Recommended]
Floor is Lava X 2.0
Warrior Monk X 1.5
Limited Slow Mo X 1.1

[1.0 Only use if it makes it easier/faster]
Paintball X 1.0
Melee Gibs Enemies X 1.0
One in The Chamber X 1.0
Scary Lighting X 1.0
Like Water X 1.0
Steelcraft X 1.0
Triple Threat X 1.0
Thrust Cannon X 1.0

[<1.0 Not Recommended] - Will decrease score
Cloaked X 0.8
Low Gravity X 0.5
Big Heads X 0.5
Enemies Explode on Death X 0.5

[<1.0 + Cheats DO NOT USE] - Cheats will result in 0 score
See Through Walls X 0.8 (Cheat)
Steelcrawler X 0.8 (Cheat)
Superkick X 0.8 (Cheat)
Super Slide X 0.5 (Cheat)
Explosive Ammo X 0.5 (Cheat)
Bulletproof X 0.0 (Cheat)
Unlimited Ammo X 0.0 (Cheat)

Leveling up is based on score. Score is accumulated in game but can also be effected by Difficulty and Mutators.

The harder the difficulty = the more points

Difficulties:
Cold Steel - Does not effect final score
Tempered Steel - Increases final score by 10%
Severed Steel - Increases final score by 20%
Sharpened Steel - Increases final score by 100%
Molten Steel - Increases final score by 200%

I found Molten Steel was too hard and sometimes I wouldn't finish the level or I'd have to try 1,000,000 times.