You will unlock the ability to perform melee Finishers after completing the story mission, "Evolution". Along with gaining the Pincer Bolt ability, you’ll also be able to purchase new powers as well, along with the Finisher melee power up. You won’t unlock the Ultra Combo ability though, until later on in the game.
When you attack enemies with the Amp, you’ll notice a gauge on the bottom left of your screen. As you smack enemies with it, the gauge will start to fill up. When it’s half way filled, you can perform a Finisher on enemies to finish them off by pressing .
An Ultra Melee Combo can be performed the same way, but will require the gauge to be filled all the way up. You'll be treated to an impressive finishing move this time around, complete with slow motion effects and extra flair.
Simply defeat 100 enemies using either of these methods to unlock this trophy. These moves will always take down normal sized enemies regardless of their health, so you will most likely get this trophy naturally due to their usefulness.