ANARCHY REIGNS

To get these trophies, you'll need to make sure you kill every boss NPC (excluding Kraken/Cthulhu, and during the 2v2 battles on White Side, both of them count) during Rampage or with a Killer Weapon attack. You'll know you did it right if you get the 10,000 point bonus Rampage or Overkill. It IS possible to get both at the same time, but it's a little luck-based. Make sure you have Rampage ready, and get the boss to low life. Immediately activate Rampage and use +. If you manage to connect and kill them, you will get both bonuses. If you're unlucky, they'll interrupt your attack with their own Rampage, and you'll be put into the button mashing sequence to kill them, which only gets the Rampage bonus.

You'll need to keep a running checklist for this, but take note that you only actually need all bosses that you would fight in 1 playthrough. Therefore, you only need one of the final set of 3 bosses, not both. If you do this in Stage Select, you can also use any character you like, so pick your favorite. For the first fight in Red Side, you won't be able to enter the fight with a full Rampage gauge, so you will want to lower their life and then turtle it out until you get a full gauge. Die if you need to, since it adds a little to gauge gain. Here's a list of relevant bosses:


BLACK SIDE
1-1: Big Bull
1-3: Baron
2-1: Gargoyle (there's 5, but as long as you kill 1 with Rampage/KW, it's enough)
2-3: Leo
3-1: Rin Rin
3-2: Zero
3-3: Max
4-1: Sasha
4-2: Zero

WHITE SIDE
1-1: Durga
1-3: Durga
1-3: Garuda
2-1: Oinkie
2-3: Jack
3-1: Fei Rin
3-1: Ai Rin
3-2: Oinkie
3-3: Max
4-1: Nikolai
4-2: Douglas (the battle ends when he reaches ~10% HP, so keep that in mind when waiting to use Rampage)

FINAL SET (a)
4-3 (Black): Max
Red Side (Black): Leo
Red Side last boss (Black): Nikolai

OR

FINAL SET (b)
4-3 (White): Max
Red Side (White): Jack
Red Side last boss (White): Nikolai