This solution will be a way to get this achievement in a full squad.
Launch up co op vs ai. Any mode works, but a quicker one like dodgeball or guardian might help so that you can end the round immdediately once you get progress. Once you enter the match, decide the order of who will get which weapon. (ex. Ashes going for boomshot)
Then head over to whichever weapon you chose, and pull out your lancer. Stay back a bit so that the bots aren't scared off from picking up power weapons. When they pick up the weapon, lancer them down. Head over and grab the weapon and you should have 20% progress. If you can, try to end the round after each person on your team gets their weapon off the bot. That way you don't have to wait for it to respawn.
Keep repeating this until everyone in your squad has this achievement, switch people going for the weapons once the original 2-3 people (depending on map spawns) have gotten the achievement. This may take a couple matches or a bit more depending on what gamemode you're playing.
Any suggestions, leave them below