Badass Mustache: Well, not quite as badass as Mario, but still quite a bit.
Big Damn Heroes: He and Yoshi get one in episode 8. In episode 9 he uses the Tanooki suit's powers to free himself from Basilisx attack and save Mario before he is killed.
ButtMonkey: He's carried this trait over from the series proper.
Iron Butt Monkey: Of course, he manages to survive most things that end up happening to him.
Foreshadowing: After being told that in the pipe maze that they could be lost forever, the professor tells him that he was just kidding, but was being serious about the pipe maze being confusing. Then, he, Yoshi, and Shadow come across a pipe that leads into a world where its really possible to end up being lost forever.
Grievous Harm with a Body: He often gets power-ups that incorporate his body, like the Blue Shell and the Tanuki Suit. He also uses his Luigi Missile.
Oh Crap: Gets an absolutely magnificent one in Episode 6.
Accidental Public Confession: While arguing with Shadow the Hedgehog shortly after Yoshi nearly being killed by Mecha Sonic, Shadow briefly mentioned Mecha Sonic. Mario overheard this and asked who Mecha Sonic was, causing Sonic to say he wished he would wait for having to explain who he is, but decides Mario needs to know.
Fragile Speedster: Sort of, he can take a hell of a lot of punishment, but his fighting style is faster paced with less "critical hits".
High Speed Missile Dodge: He did one in Episode 7, though it's subverted immediately after the dodge itself; The missile, fired by Mecha Sonic no less, did not impact him directly, but the force of the explosion did affect him, which proved to be problematic for our heroic hedgehog.
Laughing Mad: For a short while in Episode 7. Doubles as a Shout Out to Sonic The Hedgehog 3, as the sprites used were seemingly based on the laughing sprites of Knuckles the Echidna as he appeared in the aforementioned game.
Super Mode: The usual Super Sonic fair, now if he gets a hold of a Fire Flower however...
Take That: When he was 8-Bit Sonic (read: almost Classic Sonic), he made this remark.
Sonic (8-Bit): What the heck? Why am I so blocky? And I've put on some weight, too! Man, this really sucks!
Hair-Trigger Temper: He gets rather angry easily... even more so that in the actual Sonic series.
Heroic BSOD: It is heavily implied that Shadow's current characterization stems from the trauma of having to bear witness to Rouge and Omega, his only real friends, being outright slaughtered, as can be inferred from the flashback in Episode 8.
Informed Ability / Chekhov's Gun: Shadow mentions in Episode 5 that he can sense Chaos Emerald energy from long distances when explaining his suspicions about the "emerald" lying in front of him. This might act as an explaination as to how he'll find at least one chaos emerald while Mario and the others try to rescue Peach without him.
Confirmed in the Episode 9 trailer, as Shadow explicitly stated that he was going to focus himself to sense the location of the sixth emerald in the desert before being ambushed by Mecha Sonic.
Freudian Excuse: However, it wasn't his natural personality as much as him adopting it due to the trauma of his friends, Rouge and Omega, being slaughtered by Mecha Sonic.
Lightning Bruiser: Able to keep up with Mecha Sonic and put up a decent fight with him.
Memento MacGuffin: Keeps Rouge's locket with him, as shown in episode 9.
Written-In Absence: Shadow is going to be absent for most of the Omega Doomship arc because he wanted to find the Chaos Emeralds himself, realizing he can't convince them to continue finding the Chaos Emeralds and leave Peach behind at Bowser's hands.
Art Evolution: He uses Yoshis Island sprites until episode 5. From episode 6 on he has Yoshi's Island DS sprites, while all other Yoshis keep the same.
Big Damn Heroes: He pulls one of these in Episode 8 alongside Luigi, and earlier in episode 5, knocking away Thunderfoot before he can strike Mario.
Catch and Return: True to form, he can spit projectiles and whatever he can stuff into his mouth back to the sender.
Hope Spot: When he manages to catch Mecha Sonic in an Egg. It doesn't last long.
Expy: According to Word Of God, he is supposed to be this series equivalent of Cell.
Implacable Man: He's hunted those Chaos Emeralds the entire time, and has taken quite a beating, but he can still kick your ass no worse than before. In fact, he escalates it every time he's fought.
Super Mode: While his standard form can technically qualify, due to it actually being a Fusion Dance-style transformation from Metal Sonic into this form, known officially as "Turbo Mecha Sonic", he has a Semi-Super Mode with 4 Chaos Emeralds, which resembles the original Mecha Sonic'sSuper Mode, and if Alvin had not cancelled the series, he would have gotten an even stronger form with all 7 Chaos Emeralds that would have either gone by the names "Metallix" or "Master Mecha Sonic".
Breaking the Fourth Wall: Done very literally with his defeat in the second episode: After two unknown entities (Sonic and Shadow) knock away Kamek while he was holding Peach hostage, Mario capitalizes on the distraction and throws him off the racetrack by the tail. Bowser is then seen being hurled away and (in a scene taken directly from the ending of Mario And Luigi Superstar Saga) crashes into the "screen" hard enough to crack it before slipping down as if hitting glass.
Even Evil Has Standards: He did not take Yoshi's Island's destruction very well, especially when it was not under his orders.
Harmless Villain: Gets the tar beaten out of him by Mario. Again. (Subverted somewhat, because this particular scheme had him VERY close to winning and it took what is arguably a Deus ex Machina to stop him.)
Combat Pragmatist: Yes, he used the deadliest mushroom on Mario. TWICE.
Also a subversion. He states he could simply turn Mario into stone and then grind him into dust if he wanted to, and going by how he disposed of a Koopa engineer and also disabled Yoshi, Fire Sonic, and Tanooki Luigi beforehand, he certainly wasn't bluffing when he stated this. However, he makes it very clear that cutting Mario up alive is a lot more satisfying for him in regards to getting revenge on Mario.
Badass: Subverted due to the chaos emeralds power, but even without it, were way more of a threat then they were in the games.
Combination Attack: Just like in Paper Mario, they can stack up and spin. This attack is amplified with the Chaos Emerald in hand.
Continuity Nod: Their defeat by Mario was referenced in Paper Mario, and this time, they actually have a chance to exact revenge on their earlier defeat at Mario's hands (although they attempted to have revenge on Mario late in their original game, they weren't able to get the chance because Jr. Troopa brushed them away before they could fight Mario.)
Curb-Stomp Battle: They were on the receiving end of this in Episode 6. What the three-way battle between them, the heroes, and the Axems would most likely have achieved eventually was achieved in oneblow by Mecha Sonic.
Killed Off for Real: Still unconscious on the island, they were vaporized along with Yoshi's Island when Mecha Sonic charged that freaking miniature sun. They are not coming back.
Flanderization: As noted in the Too Dumb to Live section below, Yellow was even more prone to doing stupid stuff than before. In the game he was originally in, while he wasn't necessarily the smartest of the brothers, he certainly had his moments of at least cleverness, as he was the only one of his brothers who actually succeeded in (albeit temporarily) capturing Mario (by creating a makeshift "?" block to use to activate a trap door below him that leads to a jail cell.
The Starscream: After beating Mario, Sonic, Shadow, and Luigi due to their unintentionally activating the Chaos Emerald's powers, they considered backstabbing their boss (who is heavily implied to be Bowser) and calling the shots.
Too Dumb to Live: They have their moments. Like when one of them tells the Axems about the emerald radar, or when it turns out they've been holding it upside down.
These are all just from Yellow. The other 3 are much smarter. Of course, one should question why they let the dumb one hold the radar in the first place...
Totally Radical: Like in the games, they speak like they're stuck in the 90's.
Off with His Head!: The fate of Green. If that wasn't enough, Mecha Sonic even ups it by actually crushing Green's decapitated head with his bare hands.
Also, the Axem Rangers' "upgraded bodies" are that of Zero's regular form (Zero Series), Zero's Defense Form (Zero Series), A customized of the Zero model depicting Black Zero, GutsMan.EXE, and Roll.EXE for Axems Red, Green, Black, Yellow, and Pink.
Wave Motion Gun: Axem Red's secret weapon, not to mention the Blade's Breaker Beam.
The Worf Barrage: Axem Red's secret weapon, again and the Breaker Beam, again. Both times toward Mecha Sonic.
You Monster!: Red says this to Mecha Sonic after he killed every Axem Ranger, to which Mecha responds:
Mecha Sonic: "Monster? I'm not a monster. I'M A GOD."