1. Reflect 10 Projectiles
2. Meet Ness in Subspace Emissary
3. Play 5 Vs. Mode battles
While most guides I have seen online say you have to meet requirement 1 or 3 AND meet Ness in Subspace Emissary, I got him on my fifth Vs. Mode battle. Just playing 5 Vs. mode battles will clear it for you. If you want to get him with projectiles, just do a 2 player battle with Fox and Samus. Have one character use and hold down Fox's reflector shield and fire a stream of missiles with Samus. After 10 or 20 missiles bounce off Fox, finish the fight and go beat him up. As always, you can also get him just by playing Subspace Emissary Adventure Mode.
Challenger Approaching: When battling Ness, be sure to keep on your toes. If you let him catch you on fire, you will rack up a lot of damage very fast, and not be able to move for a few seconds. He can also do a good deal of physical damage if you get in close. Whatever you do, make sure not to shoot energy projectiles at him while he has his shield up. There's nothing worse than when your opponent recovers his health instead of taking damage. You fight him on Onett, where cars periodically race across the street. When I battled him, I used the terrain to help me. I got him run over by cars, and used the buildings to keep him jumping right into my clutches. I used Fox and lasered him while he was in the air too. I had him pretty well damaged when I got a smash ball and landmastered him into oblivion.
Every man dies, but few truly live. Live your life to its fullest, every day as if it were your last.