Flat Character: Character development? He has pretty much none. Tropes Are Not Bad, however, as this series pretty much focuses on how much Axel and his company can kick butt and he delivers well done.
The Hero: Is this for the whole series, but BR3/SOR3 storywise implies that he's The Lancer to Blaze.
Badass Normal: With none of Axel or Blaze's firey attacks, Zan's cybernetics or even the Charles Atlas Superpowers of Max or his young brother Skate, Adam holds his own against Mr. X's cyborgs, robots, self cloning samurai ninjas and kangaroos.
Dance Battler: While dance might not be part of her moveset, Blaze was stated to temporarily become a dance teacher before the events of 2, which could explain she makes use of various She-Fu from 2 and onwards. Also, her bio in 1 refer that her hobby is a form of dance: Lambada.
Fat Bastard: Not exactly an agile enemy, but you better not try and take advantage of that by throwing or slamming them if you're not Max or Skate (Blaze also can with her forward slam). The second game's iteration of him is an exception, though, for whatever reason.
Meaningful Name: If you need an idea of how unpleasant they are, "Onihime" literally translates into "ogre princess". "Yasha" is a term for a certain type of minor deity, but in modern usage (see InuYasha) it just means "demon".
Schmuck Bait: In SOR1, he'll ask you if you want to join him. Say "yes" and he boots you back to Stage 6. Say "yes" in a 2-player game while the other player says "no", or vice versa, and you and the other player will fight to the death, with the victor being asked the same question again.
Turns Red: Players of Remake who think they're used to dealing with his old tricks are in for a nasty surprise when he is down to his last lifebar. His stance suddenly changes to holding his tommy gun with only one arm, and he starts using melee moves like the playable characters. He even has a back throw and blitz attacks which, naturally, he can do without restrictions because he's a boss.
Muscles Are Meaningless: Granted, he uses his entire body for leverage, but even so, it's impressive how he can throw the fat mooks just as easily as Max does. Even moreso in 3, where all the adult characters are unable to accomplish that feat.
The Cameo: He's not playable in 3, but in the last shot of the good ending, he's seen hanging out with Axel and friends.
Mighty Glacier: He's slow as molasses and cannot jump to the enemy's back for the back throw. But God have mercy if he ever caught an enemy from the back, any of his slams takes out a HUGE chunk of damage.
King Mook: His palette swaps are common in later rounds of the second game. He is also accompanied by similar mooks in the third game (that thankfully only appears in the last 2 rounds) while also gains a new model (see Rocket below).
Promoted to Playable: Can be played as in SOR3 through a cheat code, albeit in a buggy, incomplete state with a limited moveset. Remake does him justice as a proper hidden character (a Game Breaker, unsurprisingly) and even features his SOR2 version seperately.
The Rival: In the remake, dialogue in one path implies that he's this to Axel.