The first level is the easiest to do this in. Before attempting this achievement, it's a good idea to max out your ammo count. You do this by collecting the hidden red skulls.
The hardest parts are the forced fights, which you can make easier by keeping everyone on one side. Hit enemies forward by pressing x,x, forward+x. You need to dash or shoot every few seconds to avoid gunfire from shooting enemies.
Some fights you can get by just by hopping on everyone's head.
The last fight you can breeze through by using one explosive barrel per group of enemies.
Spotlights only hurt you after about two seconds in them, so you can pass through them quickly without getting hurt.
Don't just retry every time you get hit. Play through the level fully so you remember where the spotlights and enemies are, and so you can develop strategies for your perfect run.