You must own the Bespin DLC to get this achievement. Sabotage mode, as well as Lando, are only available in this DLC.
There are two ways to get 20 kills with the X-8 Night Sniper:
A.) Find a Hero token and play as Lando, as that is his default weapon, and any kills you get will count towards the achievement.
B.) Complete the Hutt Contact to unlock the weapon. One of the requirements is you have to get 15 kills as Lando, so option A plays into this one regardless. If you actually manage to get Lando, play cautiously. Don't run around like you're invincible. Maximize your time with him so you can knock this out quickly.
The EE-4 is much easier to obtain. Just get 30 kills with the EE-3, get three blaster rifle streaks (doesn't have to be the EE-3, any blaster rifle will do), and complete 10 generator defense events (get a kill while near the generator in Sabotage as an Imperial, and/or get a kill near the generator after arming it as a Rebel).
Hope this helped.
EDIT: Apparently you can play Heroes Vs Villains and use Lando to get your 15-20 kills if you own the Bespin DLC. Thanks to It'z Crusher for the update!