Living Legend: Even Sonic, whom is from an alternate universe, has heard of him!
Playing with Fire: Fire Flowers. On top of that, they seem to give some flat boost to his durability and fighting skills—which makes sense, since in most games they give him an extra hit point on top of the typical Super Mushroom.
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".
Lightning Bruiser: Then again, a flashback to Mobius had him destroying one of Eggman's robotic Sonic duplicates with only a single punch, implying that he is perfectly capable of powerful upper arm strength when it comes to it.
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.
He seems to be written as the most powerful fighter of the Five-Man Band, and it shows—he's the only one able to even remotely keep up with Mecha Sonic's four-emerald Super Mode, with Mario (with his raw-power-boosting Fire Flower) managing one good hit
Berserk Button: Never mention Maria in front of him. Ally or not he won't hesitate to kill you.
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.
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.
What's worse: That wasn't even his entire attack: Shortly afterwards, he then punched Red to the Ground, punched/grabbed Red's back from below, and then kicked him into the air before vaporizing him with a beam in a manner similer to how Goku broke Nappa's back and how Vegeta killed Nappa respectively.
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".
Teleport Spam: While fighting the Axem Rangers in Semi-Super Mode, he teleported at a rapid pace as he was attacking one of them.
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.)
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.
Elite Mook: He's basically a Koopatrol on steroids.
Kiai: utilized this during his fight with Mario at one point.
Old Shame: Though Captain Basilisx was well-received by the fanbase, Alvin has stated that if he ever reboots the series he would not include him again, feeling that he was shoehorned in and would detract from the fights against Mecha Mario and the Koopalings.
Badass: Subverted due to the Chaos Emerald's 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.
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.
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.