Single Player Modes
There are a few single player modes, including the SSB classic, a new adventure mode, All star mode, Multiman melee, Sandbag, and Event Matches. The strategy for them is covered here
Classic Mode
The classic battle after battle mode, ending with a showdown against the master hand. In SSBM, the round characters are randomized although they follow the same pattern. Also, depending on what difficulty you are on, Crazy Hand(The left hand) will join Master Hand in the final fight.
Adventure Mode
A more story driven classic mode, with longer platformer levels separated by tradition arena matches.
All Star Mode
A mode where you battle all 30 characters in groups of 1,2 or 3. Your damage stays with you between matches, but there are three one-time use heart peices that you can use. Only unlocked after you have unlocked every character.
Target Test
A mode where you use a character's skills to break ten targets in a specialized arena. You are also awarded points for time taken.
Multi man Melee
These involve fighting lots of light, stupid, easy little wireframe male and female figures. The stage is a basic big platform on bottom with pyramid arranged floating platforms on top. The wireframes come in 5 at a time.
10 Man Melee
Defeat 10 of them to succeed. More of a time test than endurance.
100 Man Melee
A little harder because the AI gets smarter with the last 25 or so.
Endless Melee
Defeat more and more as the AI gets better and the wireframes get heavier. As the title suggests, it is in fact endless.
15 minute Melee
Stay alive for 15 minutes. The wireframes are endless until the time is up. The best strategy to beat this is to be donkey kong and stay in the middle of the stage and use his down+b attack the whole time. It attacks on both sides, and kills the wireframes instantly. just do this for 15 minutes and you win.
When you beat this, you get the hidden stage Donkey Kong from the original SSB.
Cruel Melee
Instead of light and stupid, the wireframes in this one are all at an AI level around 11(the real numbers stop at 9) and are super hard to knock off the stage. They are endless, but even the best don't survive long anyway.
Homerun Contest
You basically are on a stage with a sandbag and a homerun bat. Your job is to to the most damage to the sandbag without knocking it off the platform in 10 seconds and then whacking it with the homerun bat smash. It then tells you the distance you smashed it. The best way to beat this is with Yoshi. Simply jump above Sandbag and do the DownA attack about 4 times, or till you have around 120 damage. Then go pick up the bat and smash it.
If you get more than 1300 ft, then you get the Stage Yoshi's Story from the original SSB.
Event Matches
These matches are induvidual arena type matches with specific circumstances or characters. There are 51 in all. To get Event Match 51, you have to beat all the other 50 first.