The only thing you need to do for this achievement is to finish every fight with your buddy standing. It doesn't matter if they go down as long as they're up when the fight ends.
There are lots of fighting styles to choose from depending on your class, but here are a few helpful general tips to make this easier:
1. If you fail a fight you can choose 'Exit to Main Menu' from the death menu and reload your most recent save. The game automatically saves checkpoints, so you shouldn't lose much progress even if you haven't saved recently.
2. Carry extra tacos to avoid frustration during some of the tougher fights. Buy more when you run low. Farm the parking meters for change if your funds are low.
3. Get the perk that gives full health on revives--again, this helps to avoid wasting a lot of tacos in the harder fights.
4. Look for combos that let you attack all enemies for lots of damage. One I used a lot toward the end with the Jew class was fully powered Plague of Egypt with UP (frogs) or RIGHT (locusts) attacks to buff abilities followed by Cartman's Ass of Fire attack--this routinely did in excess of 10,000 damage per enemy and ended most fights before the enemy could attack.
5. You can skip side quests--the achievement pops after the main story is done. Go back and finish side quests later.