Though the amount of glitches has been highly exaggerated by critics, some of them can ruin the gameplay when you don't know how to avoid them. I own the PS3 version of the game, so I can't say that these glitches apply to the Xbox 360 version.
Wave Ocean Glitch (Sonic)
In the first level, Wave Ocean, there is one glitch at the end of the level that can be really frustrating. In the high-speed section of the level, there is a loop at the very end. If you are too far to the right, you will fall off the edge. Avoiding this glitch is as simple as staying as far to the left as possible.
White Acropolis and Crisis City Glitch (Sonic)
In the levels White Acropolis and Crisis City, you will ride a board (a snow board for White Acropolis). If you turn too hard, Sonic will freeze for a second. To avoid this, you must always push the left analog stick forward during straight paths and tilt it from the forward position to turn, rather than push it left and right from the basic analog position.
Radical Train Glitch (Sonic)
On the high-speed section, using the light dash on the first set of rings will make him run straightforward. While not entirely deadly, this does give you a 50/50 chance of staying on the ground and not falling.
I haven't played too much of the multiplayer, but when I was racing my brother on Wave Ocean, we got to a part where there was a series of springs that launched us to the next part. I was playing as Sonic, and I got through fine. My brother, however, was playing as Silver, and for some reason, he could never get across, because the springs would launch him to his doom. I'm assuming it was either because he was Silver, or because he was Player 2. There is no real way to avoid this glitch, but you can go around it by letting Player 1 (or whoever isn't Silver) go first and to get to the next checkpoint. Then, Player 2 (or who is Silver) dies purposely and spawns at the next checkpoint.
That's all the glitches I can remember.
The boss fights are 100% beatable, but can be hard to figure out sometimes. The controls are written in the form of the PS3 version, because I haven't played the Xbox 360 version.
Egg Cerberus (Sonic)
The Egg Cerberus' primary attack is that it will charge at you. When it stops and lowers it's tail,you can grind on it. Once you grind to his head, you will grab on to the horn on it's head. Now you have the ability to steer the mutt into the wall. If you hang on too long, you will be thrown off.
Sometimes, the boss will jump to the top of the stadium your in. If he does, be ready to time your jump, because he's gonna do a ground pound. The shockwave will hurt you unless you jump at the right time. Eventually, you'll grab the horn on it's head, he'll start to resist by turning around. Try to outsmart him, and you'll eventually get him.
Silver the Hedgehog (Sonic)
This boss can be extremely frustrating without knowing what to do. Silver is invincible most of the time, and trying to hit him will only cause you to be caught by his psychokinetic powers. Once you're caught in his trap, you're pretty much dead meat. The only way to beat him is to run! If you avoid him long enough, he'll pick up some tables and chairs. You'll know this when he shouts “How 'bout this?!” When he's holding the objects, he can't pick you up. Now is your time to attack! Hit him with either a home attack or a kick. As soon as you hit him, he'll drop the objects and go right back to trying to pick you up. If you repeat the process enough, you'll win.
Iblis Phase 2 (Sonic)
In this boss, you are surrounded by rock platforms. Way ahead of you are three high platforms that have orbs on them. They're important, but you can't reach them. Iblis is out in the distance waiting to attack. Iblis has two attacks: (1) He launches several meteors at you. As soon as he launches them, start running around onto different platforms to dodge them. They're most likely to land on the platforms that surround the one you were on when he shot the meteors. (2) He dives into the lava and goes on a rampage. His path is unpredictable, so you're gonna have to run from him as he breaks the platforms. When too many platforms are gone, Iblis will call in new ones that will allow you to reach the lights.
Once you reach the orbs, home attack one of them, and it'll start glowing. Iblis will probably launch more meteors at you, so you'll have to get out of the way. Because you hit the orb, Iblis will go after it instead of you next time he goes on a rampage. Once he hits the orb, he'll become paralyzed by it and will become vulnerable. Now you hit him in the eye.
You keep using this strategy until he gets down to one hit. When his health is low, the orbs become useless, and he'll charge at you differently. Stay out of his way, and eventually, he will stop in the middle of the area. Hit him one more time, and he's down.
Egg Genesis (Sonic)
This boss hovers over you, so you can't reach him. Sometimes, though, it'll lower his arms slightly. When it does, robots will appear next to the arms. Use the home attack on the robots to reach the arms. When you're on the machine, use the bounce attack move, that you've earned at this point three times on the center of the boss to hurt it.
Eventually, the center of the boss won't be sticking out, which means that bouncing on it won't hurt it. Missiles will be fired at you. Dodge the missiles, and the center will pop out again. When it's health is gone, it will try to use the last energy it has to crash into you. Just run around the area to avoid being squashed.
Egg Wyvern (Sonic)
At first, this boss, will try to shoot lasers at you. Just dodge the lasers by avoiding the target marker. Soon, it will charge at you. Once it's head is in range, home attack the head to grab onto it. Like the Egg Cerberus boss, you have to steer it. Only this time, you have to steer it into floating chunks of metal.
After every hit, the boss will shoot electric missiles that will destroy any platform it lands on. Then he'll fire a series of red lasers at you. Once again, running around is the best way to avoid these. Some times, he'll use a homing laser. As long as you stay far away from it, you'll be safe from this attack.
After a while, he will stop swooping in to attack you and stand outside of your reach and taunt you. He will have two little robots in front of him. Home attack the robots to get to him.
The final blow is as simple as hitting the head before he slams into you. Now you have beaten Sonic's story.
Iblis Phase 1 (Silver)
On your platform, you'll have plenty of things to throw at him. Just hurl as much stuff as you can as he tries to get near you. Your more likely to hit him if you throw after a jump. If he throws rocks or building chunks at you, hold down the R1 button to pick them up and throw them back with square.
Sonic the Hedgehog (Silver)
Sonic the Hedgehog is a simple boss. His only attack is that he tries to home attack you. Just throw stuff at him with you psychokinesis before he hits you. You can pick him up, but you can't harm him.
Egg Genesis (Silver)
It's rather simple. Pick up stuff and throw it at the core at the bottom. You are more likely to hit it if it is closer to the ground. Sometimes it will shoot lasers at you, and the ground enemies try to get in your way. Use the missiles the ground enemies shoot at you to your advantage by picking them up. At the end, it will try to crash into you like it does in Sonic's story.
Shadow the Hedgehog (Silver)
Beating Shadow is basically using the same strategy as beating Sonic (see above). It should be noted that Shadow can hurl tornadoes at you. If you get too close, he'll throw his chaos spears at you. Later, he will use Chaos Boost to get stronger.
Iblis Phase 3 (Silver)
This boss is very similar to Phase 1. He throws stuff at you; you throw stuff back. The boss is significantly harder, because if he gets too close, he'll destroy part of your platform. If this happens too many times, you're history. When he smashes part of your platform, you can use your psychokinesis on his head to give a devastating blow. Wait for Blaze to tell you the first time, or look for the mark on his head that show where to hit him. Though throwing rocks may seem insignificant because of this attack, it is important because throwing rocks will help lower his health before he completely destroy your platform.
Sometimes he'll throw rocks like Phase 1. As with Phase one, hold the R1 button to grab some rocks.
Sometimes, he'll throw a humungous meteor. If this thing hits your platform, it's an automatic kill. So how do you stop it? It turns out, if you hold R1, you can actually catch it! As usual, throw it back to give him a monster headache. Know these tips, and the boss shouldn't be a problem. Now you have beaten Silver's story.
Egg Cerberus (Shadow)
Almost exactly the same as Sonic's encounter with the boss (see above). It has one extra attack where it tries to stomp on you.
Iblis Phase 2 (Shadow)
Once again, almost the exact same as the fight on Sonic's story. The only difference is that the last rows of platforms are not replaced when destroyed until just before the last of Iblis's attacks.
Mephelis the Dark Phase 1 (Shadow)
Mephelis is your shadow (ironic isn't it?), so you can't harm him. You'll have to defeat the little black pests around you until you Action Gauge is full. Once it's full, activate your Chaos Boost to get Mephelis out into the open. Sometimes, he'll block your attacks. If he's attacking you, you can hit him.
Eventually, Omega, Shadow's robot buddy, will come out, and you'll have to play as him. Ignore the little pests. Just attack Mephelis.
Silver the Hedgehog (Shadow)
It's the same strategy that you use in Sonic's story. (Shadow certainly has a way with copying other characters' bosses.) Shadow's chaos spears can know him over, but prove useless if you're trying to harm or stun him.
Mephelis the Dark Phase 2 (Shadow)
First, you just need to avoid the stuff falling on the ground. Mephelis is currently invincible. Next, you attack the big, scary shadow creatures to gain Action Gauge energy. The creatures will shoot lasers and slam their heads into the ground to try to stop you. If you throw a chaos spear, you can stun them. Then you do a Home Attack combo.
Once your gauge is full, activate your Chaos Boost. Mephelis will reveal himself, which will give you the chance to attack. He will clone himself, but the real one is the one that's creating the ball of energy.
If you run out of Action Gauge energy, repeat the process mentioned in the first paragraph of this boss.
Once he's down to his last hit, Mephelis will create clones of himself in a spiral where he's at the top. Home Attack your way up to the clones and deliver the final blow. Now you have beaten Shadow's story.
Solaris Phase 1 (Final)
You are given the ability to play as Super Sonic, Super Shadow, and Super Silver. To change characters, you press the triangle button. Each character has 50 rings that slowly drain. Switch to another character when you're running low. The previous character will start to regenerate.
Soon you will realize that you can't hurt him as Sonic or Shadow. That's because the boss has a specific order of who to play as.
First, you play as Silver. Solaris will throw meteors at you. Hold R1 to pick them up, and then throw them back with square. Continue to do this until a part of his armor cracks. Then switch to Shadow.
As Shadow, you hold down R1 to charge your energy. When it fills, press square to hurl several chaos spears at him. Once another piece of his armor cracks, switch to Sonic.
Finally, as Sonic, hold R1 to charge your energy. Once it's full, press square to charge at Solaris. Keep doing this until Solaris is defeated.
Remember that pressing the X button will make your character go faster. This can be useful to dodge attacks.
Solaris Phase 2 (Final)
In this phase, Solaris will block any attack when he's standing still. If he's shooting lasers, you can hurt him. This phase allows you to play as any of the three characters. Silver, however, isn't quite as useful as the other two. Once he's out cold, you will have beaten the game!