The three main 1 player modes are Classic, Adventure, and All-Star, which is unlocked when you unlock all 25 characters.
Classic Mode
Classic is divided up into several fights, structured similarly to the first SSB, but more random.
Difficulties listed from 1-10
Fights 1, 3, and 5: Vs. a single opponent
Very Easy: 1
Easy: 2
Normal: 4
Hard: 6
Very Hard: 8
Fight 2: Two-on two battle
Very Easy: 0
Easy: 1
Normal: 4
Hard: 8
Very Hard: 10
Fight 4: Three vs. one giant
Very Easy: Sit back and laugh
Easy: 0
Normal: 2
Hard: 5
Very Hard: 9
Fight 6: Vs. a weak team of one character
Very Easy: 0
Easy: 1
Normal: 4
Hard: 8
Very Hard: 10+
Fight 7: Vs. a metal character
Very Easy: Comical
Easy: 0
Normal: 3
Hard: 6
Very Hard: 10
Fight 8: Vs. Master Hand and possibly Crazy Hand.
Very Easy: 2
Easy: 3
Normal: 4
Hard: 5
Very Hard: 7
With Crazy Hand
Normal: 7
Hard: 9
Very Hard: 10+
Fights 1, 3, and 5 progress linearly from Very Easy through Very Hard, fight 2 progresses at a steeper rate, there's a huge gap between Normal and Hard in the giant fight (in Very Easy, the giant fight is funny to watch), there's also a huge gap between hard and very hard in the team fight, and the metal character becomes progressively harder (in Very Easy, the metal character is funny to battle against because they're easier than a normal character). Master Hand's difficulty depends on the level you're playing, obviously. Ironically, on Very Hard, although Master Hand is most difficult, if you're not fighting Crazy Hand, it's the easiest battle of the bunch.
Very Easy: 150 HP, weak attacks Easy: 250 HP, weak attacks Normal: 300 HP, average attacks Hard: 330 HP, strong attacks Very Hard: 360 HP, very strong attacks plus high attack rate
Adventure Mode
The difficulty of each is ranked out of 10 with 1 being the easiest and 10 the hardest.
Mushroom Kingdom Adventure
Mushroom Kingdom: Defeat Goombas, Koopas, and a Yoshi team along the way. All the enemies are light, so should fly far. Note, though, that when fighting the Yoshis, that if you fall off the platform you will lose a life. If your time ends in a 2, the next battle will be against Luigi and Peach and not Mario and Peach.
Very Easy: 1
Easy: 1
Normal: 2
Hard: 5
Very Hard: 8
Peach's Castle: Fight a team of Mario and Peach (or Luigi and Peach). The people who designed this stage were butts because they seem to complement each other and follow each other, with Peach usually opening the attack, and with such a difficult stage being so early in the game, it can be VERY discouraging to play, causing a fear that one will need to pay a continue fee near the end, even on Normal mode. Luigi is a better fighter, but has a higher tendency to suicide with his Green Missile. Your best bet is to spam them with a clear out move.
Mario battle
Very Easy: 1
Easy: 3
Normal: 5
Hard: 7
Very Hard: 9
Luigi battle
Very Easy: 1
Easy: 4
Normal: 6
Hard: 7
Very Hard: 8
Kongo Jungle D.K. Rap
Kongo Jungle: You start the stage having to fight two tiny Donkey Kongs. Fortunately, their small size is not a big impediment to your success (as in the Event Match Lord of the Jungle), and they fly far when you hit them, so this battle isn't very difficult.
Very Easy: 1
Easy: 2
Normal: 3
Hard: 6
Very Hard: 9
Jungle Japes: In this match, you fight a giant Donkey Kong. He's easier than he looks-get in close and keep pounding him. Sometimes, he will go under the boards and get KO'ed by a Klap Trap.
Very Easy: 1
Easy: 3
Normal: 5
Hard: 7
Very Hard: 8
Underground Maze/Lake
Underground Maze: Defeat Redeads, Octorocks, Like-Likes and up to 5 Links. You are supposed to find the Triforce, and it is in one of six locations. If you go to the wrong place, you will have to fight Link. It is possible, though, to avoid them by careful jumping, but you will get 30000 bonus points for defeating all five.
Very Easy: 1
Easy: 2
Normal: 5
Hard: 7
Very Hard: 8
Hyrule Temple: Fight Zelda, on easier difficulties she's a pushover, but on higher difficulties she seems to have perfect aim all the time, so shield often.
Very Easy: 1
Easy: 2
Normal: 5
Hard: 8
Very Hard: 10
Brinstar WARNING
Brinstar: Fight Samus. It shouldn't be too hard except in higher difficulties.
Very Easy: 1
Easy: 3
Normal: 5
Hard: 9
Very Hard: 10
Escape: Escape Brinstar in 40 seconds.
All difficulties: 4
Green Greens Kirby Hat
Kirby: This is a regular battle against Kirby. He isn't very hard.
Very Easy: 1
Easy: 2
Normal: 3
Hard: 5
Very Hard: 8
Kirby Team: Each Kirby has a unique copied ability. They are much weaker than the first Kirby, but stay alert because the damage adds up!
Very Easy: 1
Easy: 1
Normal: 3
Hard: 7
Very Hard: 10
Giant Kirby (special conditions): Giant Kirby fights like regular Kirby. Beat him the same way.
Very Easy: 2
Easy: 5
Normal: 7
Hard: 9
Very Hard: 10
Corneria Race
Fox 1: This battle is a regular battle against Fox at Corneria, except that there are no Arwings. Fox is fast, but he can't take much punishment, so try to stay on the offensive for this one. If you have Falco as a playable character, then you may fight either of the two.
Very Easy: 1
Easy: 3
Normal: 5
Hard: 7
Very Hard: 9
Fox 2: In this battle, there are Arwings to help Fox/Falco win. This battle is usually easier than the first one because Fox/Falco can be KO'ed by the Arwings. Staying away from the lasers is more important than defending yourself from Fox/Falco in this battle.
Very Easy: 1
Easy: 2
Normal: 4
Hard: 8
Very Hard: 10
Pokémon Stadium Battle
This is a very difficult battle because you have to KO twelve Pokémon with no breaks in between. Many Poké Balls appear, however, and if you can get to them before your foes, the prizes inside should help you a great deal. However, on Very Easy this should be as easy as the Team Yoshi and Team Kirby battles, but on higher difficulties, you'll probably need a continue here.
Very Easy: 1
Easy: 3
Normal: 6
Hard: 8
Very Hard: 10
F-ZERO Grand Prix Race
F-Zero Grand Prix: Avoid the cars and jump over all the ditches without getting hit. Land on every third or so platform.
All difficulties: 5
Mute City: Fight Captain Falcon, just don't leave yourself open and you should be fine. What makes him a pain is that he's very fast and a heavyweight at the same time. Luckily his attacks are slow.
Very Easy: 2
Easy: 4
Normal: 6
Hard: 8
Very Hard: 10
Onett Battle
Fight three Nesses. On the easier difficulties they fly far and are weak, but on the harder difficulties it's a standard 3 on 1 battle.
Very Easy: 1
Easy: 2
Normal: 5
Hard: 8
Very Hard: 10
Icicle Mountain Adventure
Play through the Icicle Mountain stage and then fight two teams of Ice Climbers.
Very Easy: 1
Easy: 3
Normal: 4
Hard: 6
Very Hard: 8
Battlefield Metal
Giant Wire Frames: These wire frames are huge, but they fly very far when you hit them, and their attacks aren't that powerful. The low gravity makes this battle even easier. A nice break from the tough battles you've faced before.
Very Easy: 1
Easy: 1
Normal: 1
Hard: 3
Very Hard: 7
Metal Mario Bros: Metal Mario appears in this battle, and so does Metal Luigi if Luigi has been unlocked. Although they can take a great deal of damage, they are slow, and they fall very quickly if you knock them off.
Very Easy: 1
Easy: 2
Normal: 5
Hard: 9
Very Hard: 10
Final Destination Bowser
Bowser: In this level, you must KO a slightly-larger-than-normal Bowser. He has a little more endurance and power than the regular version, but his speed hasn't improved at all. Use the same tactics that you use against the regular Bowser.
Very Easy: 1
Easy: 3
Normal: 4
Hard: 7
Very Hard: 10
Giga Bowser (special conditions): If you beat Bowser on Normal or harder within a certain time limit (measured over your entire adventure), you have to fight Giga Bowser, who has more endurance and can deal more pain than the one you just sent flying. Be prepared for a very difficult battle.
Normal: 6
Hard: 8
Very Hard: 10+
Hard Mode
In order to get the Crazy Hand trophy, you must beat Adventure in Hard or Very Hard mode without using continues. Doing it hard mode classifies you as a gluton for punishment, so stay away from very hard unless you want the undeniable bragging rights. Several easy methods will make the conquest significantly easier. First and foremost, DELETE EXTRA CHARACTER DATA! This helps you most at Battlefield, where you will now only need to fight Metal Mario instead of the Metal Bros., but also spares you from fighting Pichu at Pokèmon Stadium (you may want to re-unlock Jigglypuff if you feel it will make that battle easier. I didn't) PLEASE NOTE! After doing this, I am having trouble re-unlocking Mewtwo. Maybe you should wait resorting to this until I research this more. Secondly, stall as long as possible (five or so seconds left on clock) at Mushroom Kingdom, Underground Maze, Escape from Zebes, and Mute City (Wait on the last platform). By doing this, you are sparing yourself from fighting Giga Bowser. It is hopeless if you fight Giga Bowser. Other from this, make sure you know what you're doing, be conservative with the damage you take, don't take too many risks, and keep a bottle of asprin ready. It may help to go through the whole thing with continues to familiarize yourself with the battles.
All Star Mode
All-Star mode is unlocked when you have unlocked all the characters in the game. In All-Star mode, you will only have one life to face all the characters in the game. You will have a break in between fights to heal, but you can only heal three times. This mode is very challenging on Normal, Hard, and Very Hard, and you may need continues. You start out going one on one (in the first four fights), then one on two (your next four), then one on three (four more). At the end, you will face a army of Mr. Game and Watches. Trophies will sometimes appear between matches.