To earn the achievement "Challenger", you must play at least ten ranked matches.
To find this mode, go to the main menu, then select Xbox LIVE BATTLE, then when the next screen pops up on the screen, select Ranked Match.
Select your character, then play against ten fighters. It can be anybody on XBox Live, whether you fought them before or you haven't fought them before. It also doesn't matter if you win or lose; as long as you play the entire match from start to finish, win or lose, it will count. From your first match, play the next nine matches normally. Once you win or lose the tenth ranked match, the achievement unlocks for good!
If you're having trouble finding opponents to take on in Ranked mode, just switch the settings to "Worldwide" and you should be hooked up with no opponents all the time in a jiff! Credit for this tip goes to OzzysShadyDisco!
Have fun and good luck!