GameTrailers has a great walkthrough, here is the first entry:
To beat No More Heroes 2, you must work your way up through the ranks to become the #1 assassin. Your first battle in the game is against the 51st ranked assassin, but thankfully you do not have to kill all 50 of the remaining assassins standing between you and first! Read below for strategies on beating the assassins you do have to defeat in order to win the game.
When you first have control of Travis Touchdown, you’ll be facing an albino enemy, Skelter Helter, the brother of some poor fool you slaughtered in the first No More Heroes. This guy is no pushover. The game will run you through the controls here throughout the fight, so pay attention to learn the various battle techniques available to you. Lock onto the guy, run toward him, roll out of the way of his attack, then start hacking away until he drops.
After a gratuitous fan service cutscene, you’ll be back fighting Skelter Helter. Go to town on him before he starts firing his gatling revolver, then go crazy on him with your beam sword again. Use a combination of high and low slashes, and move the analog stick in the directions indicated onscreen, when they make their appearance, to finish the bastard.
You’re now the 51st ranked assassin!
Another few cutscenes rife with sexual innuendo violence later, you’ll find yourself in your apartment. Play with your fat cat, Jeane, or choose your wardrobe, or play a shmup, or whatever you feel like. When you’re ready to get on with the game, exit the apartment. If you feel like tackling a Side Job, by all means do so. You can also visit Airport 51 (to buy new clothes), Naomi’s Lab (to buy new weapons), or Ryan’s Gym (to build up your strength & stamina). We suggest at the very least playing the Side Jobs to earn enough money to purchase the new weapon from Naomi.