For this trophy you need 100 kills with the Razor ship. Here's a few tips based on how I like to play the Razor and hopefully it helps.
First some basic information, the Razor is a scout ship which means it has low health but it moves fast and captures outposts at a dramatically faster speed. The Razors primary weapon is a 2 shot launcher that can be locked onto enemies, it does moderate damage but is unreliable, as soon as you level up your razor disc and teleport you'll be good to go.
Now the build, definitely mostly be using the razor disc and teleport ability, The priority is maxing out the razor disc and teleport, I usually put a point in core just after I've gotten the disc and teleport to level 2, this is all the core you'll need.
When playing the Razor you'll be getting in close and taking risks, this class isn't really for those who play cautiously. You can opt to max out the primary weapon and spam it at range and pray you get the last hit but it's pretty hopeless. You'll want to fly right in and use the razor disc and teleport through the enemy when your disc is about to fade for a final dash of damage, this will kill many smaller ships, against combat ships you'll have to repeat this process over and over. In some circumstances you'll want to teleport towards a fleeing opponent and use your razor disc to finish them off. Against big ships if you keep dashing through them and being unpredictable you can really annoy them and make them feel hopeless as you chip their huge health down to nothing.