Go to Options > Game Settings and use these settings:
Difficulty: 1 Star
Damage Level: 8 Stars
With the above settings, the AI should go down quickly, and without putting up much of a fight. My favorite thing to do is save up enough meter for a duo team attack ++. A duo team attack requires at least 2 meters. When you're in this mode, both your characters are on the screen at the same time and you have unlimited meter. Spam both your characters hyper combos as much as you can to score a quick KO.
That was the easy part. The hardest part will be the final boss, Onslaught. It may seem impossible at first, but like most boss characters, there are certain patterns that he'll fall into, which you'll learn and be able to take advantage of.
There are two phases in this fight. Note: You do not recover health between phases.
Phase 1: Assist selection is important. It'll help you deal alot of damage and you won't have to risk taking as much damage during the first phase, which will give you a much better chance of beating phase 2. I recommend Psylocke because she comes out very fast, does alot of damage, and can be used 5 times. Start holding + BEFORE the assist menu appears to choose Psylocke.
Onslaught will do many fast, high damage attacks that are difficult to telegraph. However, there is a small period of recovery after he does each attack. Block until he teleports or charges in front of you, and immediately press + to call your assist. While he's being hit by your assist, sneak in a few hits with your point character. Wait for him to attack again and repeat.
Watch out for his hypergrav move. It's unblockable and sucks you in and he'll follow up with a ton of damage. Either jump over it or hit it with a projectile or attack.
Phase 2: Save your meter for the second phase. In phase one he recovers fast enough during a hyper that it won't fully connect and ends up being a waste of meter.
Now aim for the head. His arm can be hit as well. It's a good idea to have at least one character that can do hypers in the air like Ryu and Megaman. A couple of well placed hyper combos to the head should be more than enough to finish him off. Again, try to attack when he's recovering from an attack. Scoring enough hits (hypers are good for this) will stun him and interrupt his attacks.
If you're going for "Crossover Legend" you can hit on a second controller to start a local match and save yourself whenever you think you're about to lose. Otherwise, you can use as many continues as you want. You can also switch characters whenever you use a continue. If there's a team your comfortable with, you can use them up to Onslaught, lose, use a continue, and switch to the characters you need to beat the game with.
Also note that when you complete arcade mode it will count for BOTH your characters.
You can also see a complete playthrough by RA1NKING HERE.