To clarify, you don't need to get 20 kills with both weapons. It's actually 20 kills with either/or, or a combination of both. I have only the A180 unlocked and I'm 80% of the way there. I would suggest not wasting your time with the Sonic Imploder unless you really really want it, since you need 15 Impact Grenade kills as part of the requirement to unlock it and it's a pain in the ass to get those.
And yes, this is a DLC weapon, so you must complete the Hutt Contract first. 30 Heavy Blaster/30 Heavy Pistol/30 Targeting Rifle kills.
Or, as c1w suggested, you can just play as Jyn Erso in Heroes Vs Villains or Hero Hunt and farm kills there.