You will no doubt kill a few aliens over the course of the game but will likely need to grind the remainder.
An easy place to grind is within a Hard difficulty Super Powered Fightclub activity, there is one in the centre of the map (Shown in the video) start the activity and complete the first wave.
Now you'll start the second wave which is King Of The Hill, ignore the hill and instead stand on an open flat area. Several men with bats will continuously come for you and agro to you now which is perfect as these still count as aliens. Make sure you have the Stomp super power selected with
and then press
to stomp the ground, hopefully they will die from the impact/colliding with a wall as they are low level aliens. (You may need to jump before Stomping else them hitting you will interrupt your attack)
You have plenty of time on the counter to get all 150 but if you happen to fail make sure you EXIT the activity to start over else your kills will not count for your challenges (Though the achievement tracker will keep progress)
Here's a video