I've been seeing a lot of short clips of anime content recently and some of the move/attack combinations look REALLY cool! I'm trying to theorycraft something that will look like that by around level 12 so I don't have to wait all game for it to come online. I'm looking for martial ideas or martial hybrids as opposed to pure casters. So far I have the following:

1) Battlemaster Fighter/Gloomstalker Ranger (Tabaxi): 1st round is essentially Zephyr Strike, Feline Agility, move to the enemy, Trip Attack to (hopefully) knock them prone, the rest of the attacks are at Advantage. 1st round also grants extra Move, an additional Attack, and an extra D8 of damage from the GS Dread Ambusher.

I like this one because you can make your approach from FAR away for the opening strike.

2) Samurai Fighter/Vengeance Paladin (Var Human): Bonus Action for Fighting Spirit and Advantage on all attacks for the round. Pally Smites all around and I can even see this one having some of the epic FX that many of the Anime have.

3) Bladesinger/Gloomstalker Ranger (Elf): Bonus Action for Blade Song, rush to attack with Green Flame Blade or Booming Blade. Use the Revenant Blade Feat and the Double-Bladed Scimitar for extra flavor. Of course, this one would benefit by a 2-level Fighter dip for Action Surge.

What else does the Collective have to offer?

I've got a first round for a plain old Barbarian I thought was pretty good. The party was ambushed in a tight alleyway, with three archers on balconies above. My barbarian Raged, jump onto some boxes, jumped up to a balcony. At this point, the GM decided it would trigger an opportunity attack from the guy on the balcony. He had a bow, but his attack was to try and shove me off - fair's only fair. I asked to spend a reaction to try and pull him off instead as he tried. This was granted, and the first guy fell to his death on the unforgiving cobbles below. Then, another jump to the next balcony - across the street - where I severed another archer straight down the middle with my greatsword. 

Out of actions, but on the next round my barbarian went into the apartment, and crashed straight through the rotting plaster walls of the slummy tenement, to face off against the last ambusher. He informed the poor guy that his tribe had a tradition for naming a new weapon for the first enemy it killed. And thus, he gained a blade called Shane. Obviously, that wasn't the greatsword - he pulled a dagger for this specific purpose. 

I felt it was way cool to ask the man his name, just so I could name the weapon I used to kill him. 

4e was so good for this, because you had daily powers that were super strong but you could only do once. There was a whole "alpha strike" meta that centered around this concept. I had a monk that could punch someone 30 feet into the air, then leap up and slam them back down to the ground.

To replicate this in 5e I suppose you could hit someone and grapple them with the Grappler feat, jump up into the air via Boots of Flying or something, and then hit them again and drop them and you'd still have a bonus action to add some more flair in there somewhere.

Wouldn't the most anime thing be to spend five minutes giving a speech about how you vow to defeat the villain this time as you furiously close the ten foot gap between the two of you?

Don't forget that the villain gets to talk too.

And how do you do the whole normal guy transformation sequence into super hero thing?