I saw the other guides, and while they are quite helpful in some areas, not everyone has the skill or patience for every other AAA in the game. I will try to make this guide as complete as possible, with tips for pretty much every world in the game.
To get a AAA in any game, you will have to do twice or sometimes even thrice the time/score/whatever than the A rating requires.
As the other solutions said, you're pretty much better off using Eggman for almost all SEGA Games. Why? Because he has high power and good control, which means accuracy. For speed related games, like running from police or zombies... or balls, use any speed character. Whichever character you use for speed is your choice. I know that other solutions suggest Control characters for the Jet Set Radio games, but since it took me little over two days of grinding to finish my AAAs, I was used to Eggman, so I did it with him and everything went alright.
As other solutions mentioned, tournaments need to be won flawlessly, but you can restart the match you are in by just hitting retry without having to restart the whole tournament. To be able to win a Tournament or Match, just keep in mind, the AI can make mistakes, the trick is to make them make those mistakes for you to throw them off the other direction and get the point. For every match in a tournament or regular match you need to basically score 8 points in a row, and one of them is a free point due to the Special Star Attack Thingy. Yeah, that sounds about right.
In-game music sucks. Play your own music. I beat Alex Kidd listening to my favorite Duran Duran album. If music doesn't help you concentrate, then just turn it off completely.
Also, try to get close to the net, especially with Alex Kidd. If/when you control the net, you can basically lead the AI anywhere and do a power shot to the other side for easy points. Try to stay in the horizontal middle to avoid any sneaky side shots by the AI.
AI difficulty varies, just because a character is hard in one match, it doesn't mean he/she will be hard in another. You can calculate the difficulty by looking at the power of their serve. Don't let this panic you, though, some AI's with powerful serves can be easy to win against flawlessly.
To win specific matches, just remember your controls:
LS - You use this to walk around, but more importantly, to lead the ball. This is an important detail for accuracy related games, imagine the center point of the other court as LS standing still. Every direction sends it to the respective relative direction from the center point of the other side of the court.
A - Topspin, great and rapid all round shot, and a good power shot for the sides. Hold before the ball gets to you for better results.
X - Slice, good side shot but a bit slower than A.
A, X - Lob, basically throws the ball up in the air to the back of the court, it's great for leading the AI to the back of the court. Be careful, if you lob from the net you're risking an out. This one isn't used much in accuracy-related games.
X, A - Drop Shot, truly a beautiful shot for winning games, it's slow, short, and painful to the AI if they're not close enough. It also works well to lead the AI close to the net to a corner and then Topspin towards the other side for an easy point.
X or A when returning a lob - Smash, easy point gainer. If the AI throws a lob, you will see a ball growing smaller on the floor. Get close to it and smash the ball for an easy point.
The worlds are in alphabetical order.
Includes a simple Singles Tournament like any other. You get Alex Kidd in the second match, but he's not as difficult as in the Alex Kidd tournament, so don't panic and remember the tips above, you should nail this one in no time.
Just a simple tournament, right? Wrong. Alex Kidd is the last opponent. It is easy to get to him, but winning against him is a tad bit tough because he is cheap and fast. Be VERY careful not to do lobs, because he could smash the ball and you'll have to restart. Be careful when HE lobs as well, but if you're still a bit far from the net, his lob could end up being an out, good for you, right? Just have patience, learn his moves and use drop shots and side power shots wisely. Remember to retry if the AI scores.
You basically lead robotic mice to a rocket. Yes, you read me right, robotic mice to a rocket. The tennis part of it is that you have to hit balls to switches that lead the mice. Every level is the same, no matter what there is no randomness. That is good, because you can just press start at the beginning of a round to look through the transparency at the switches and general layout to see which approach you should take. Remember that:
-Switches move clockwise when hit.
-When mice hit a wall they move right, if a switch is pointing towards a wall mice move right as well.
-Cats can be easily killed by getting hit. SImple as that.
-Use LS as explained in the controls, just point from the center towards whichever switch you need to hit.
-Take care of the closest switches to the mice first, then the closest to the rocket.
-Don't try to control everything. You basically get a minute per round in the round based games, take your time to make the mice go to the correct places.
-You can stick one group of mice in a cycle between two switches while you concentrate on the other group, if the rocket isn't there yet.
-For the "Score With ChuChus" game, you just have to finish all the rounds. You get 1 minute per round no matter what. The time bonus is for the score.
-For the "Everybody Moves" game, just point all the arrows to the middle, and rockets should appear appropriately for mice to go in after never-ending cycles.
-Every other game is straight up, just be quick at the start, and remember to press start to look at the general layout.
ZOMBIES! I really enjoyed this world. Basically, just use lots of A power shots. Eggman, as mentioned before, works awesomely with power shots. Just remember to hold A before the ball gets to you, then release at designated zombies for the desired effect. Grab powerups when available, this one is a fun world to AAA. The big ball is not a great powerup, though, but grab it if nothing else is around. Try and take care of zombies close to you first, so you don't get killed.
Again, straight up singles tournament. Not too hard if you follow the tips mentioned at the start of the guide.
Jet Set Radio
This is probably the hardest world in the game. You basically have to paint tags in some activities. You have to be skillful, accurate, and most of all: lucky. The other guides cover this world very well, but I will do it myself as well.
Again, just remember the following:
-Use LS accordingly, tags can appear at the bottom, center, or top of the court, and sometimes on sides as well. For tags close to you, use A shots with LS pointing down, and use drop shots only if needed for corner bottom shots.
-For center tags, point LS up in the desired direction, then down. Don't ask me why, but it works that way
-For top tags, point LS as far as you can to that direction, if you get a vertical tag (which has top, center and bottom letters), just use LS accordingly to the letters.
-Be very patient, you may not always get the colors you need. If you get hard words in the beginning (those are: Ulala and Eggman), unless you know you have the skill for them, it is better to retry. You can always just practice on them as well, to get used to them before concentrating on AAA ratings.
-Same color letters can be painted with one shot if they connect and you hit the center point. Very helpful to save time, but not required for AAA.
"Hit Combo" - This level is tricky, but I have a killer tip to help hit the guy on the skateboard. Move to the top left corner, with a little bit of space from the net of course. This'll make hitting Combo 1000 times easier, because you'll basically have a small area to hit him in. Try it out multiple times and you'll get this one in no time. You need about 8 or 9 Combo hits for AAA.
"Tag Attack: Expert" - This level is kind of a pain. You have 2 minutes to paint 6 tags. You most of the time get hard tags, but occasionally easy ones. Keep retrying and eventually you will get a run with easy tags. Take a few times just to practice tags, without concentrating on the AAA, so that when you do you know the tags accordingly.
"You Got Graffiti Soul" - You have to finish 7 tags WITHOUT MISSING! I know it sounds hard, but they are mostly easy to medium level tags, so basically practice doing them perfectly before doing the AAA run. Time stops when you finish a tag to let you pick up the trophy thingy... or whatever it is you get when you finish a tag perfectly, it just looks wierd.
"Avoid Rokkaku Police/SWAT" - Basically grab a speed character and run in circles. After a few seconds, the Rokkaku guys will move down and leave while others spawn at the sides, so just look for open spaces and either stick to the bottom or top of the court when the center is filled with them.
A couple of matches and a tournament, simple to AAA with the tips at the beginning.
A Doubles Match and Singles Tournament. Straight up, simple.
Your everyday stacking arcade game. You hit the slimes to clear them, and if there are more than one of the same color touching, they all clear at the same time. Try to keep rebounds going, because serving the ball really takes a chunk of time, which isn't helpful for AAA. White Puyo are garbage Puyo, just hit adjacent Puyo to clear them. If you hit garbage Puyo, the ball just bounces, which is helpful for the "Rebound The Ball" game.
"Rebound The Ball" - Wait a bit before serving, so that more puyo fill the wall. Time doesn't start until you serve, but don't take too long or the wall will fill completely and you'll have to retry.
"Clear 4+ Combos" - Keep rebounding the ball on single Puyos until you see a 4+ Puyo group, then smack the hell out of it.
"Clear The Puyo Wall" - Just learn where to hit the wall after each rebound. Just know that each wall has an easy way to finish it. You can make mistakes, but don't waste too much time. You get enough walls when you finish the first wall with purple Puyos for AAA.
Samba de Amigo
Straight up Singles Match and Doubles Tournament. Quite easy, as Amigo is an AWESOME partner. Just remember the tips at the beginning.
Sonic The Hedgehog
Most of these levels are speed related, so just use a speed related character. Very straight up, just collect rings, avoid balls, return balls, etc. For avoiding balls, just try to predict the ball's trayectory and avoid it. If avoiding balls AND collecting rings, remember rule #17: Don't be a hero. Wait for the right moment to get the respective rings.
Space Channel 5
Straight up Singles Tournament and Doubles Match. Should I repeat myself again? Sure Mr. Red, go ahead! Ok, just remember the tips at the beginning of the guide and you should be fine. Just one thing to add: try not to let Gum play with the ball too much in the Doubles Match, she sucks. Really, I cannot tell you how many times i had to retry due to her screwing up a shot.
Welcome to the fantasy zone! I hate that sentence now. Part of the reason why I told you to turn off the music, you should probably turn off the sound as well in this one. You basically get wierd and abstract stuff flying all around, which you can shoot with your balls. It takes some practice to get used to the shooting in this world, but it's simple once you get used to it. Again, try not to get killed. If you can't take the shot, move away instead. For the tomos (circles that open) don't wait for them to open before you shoot, learn how long they take to open, and shoot little less than a second before they open for better results.
Super Monkey Ball
Now, this world has gone Bananas! Hehe, see what I... fine, don't laugh at my stupid jokes. Jerk. You basically hit giant balls with your balls to throw them into gates.
"Get Bananas!" - You throw the balls into gates to spawn bananas on your side of the court. All I can say is, concentrate on hitting the balls into gates and grabbing bananas separately. What I mean is, first get a lot of balls into gates to spawn lots of bananas, then grab them all at the same time. Easy peasy.
"Clear The Moving Gate" - This one is kind of tricky because the gate is... well... moving. Just get lots and lots of rebounds, and hits the balls to where the gate will move, not it's current position. Also, getting the balls into corners as a group can help as well.
This one was actually pretty fun. It's like a shooter, but with tennis balls.
Things to keep in mind:
-You have infinite balls, keep on shooting on the score based games cause it doesn't slow down your reticle, unless there are civilians in the area. Don't do this for "Make Every Shot Count," though.
-Justice shots are shots to the enemy's gun, just sayin'.
-The reticle slows down when you get close to an enemy, very helpful for being accurate.
That's it for today's guide! If you have any questions or requests, feel free to comment below. I will get to you as soon as possible. By requests I mean if you want me to cover a certain game or to include the score needed for AAA rating.