As simple as this achievement sounds, you must gain level 20 on a strike team while in Single Player. i.e, goes Ding when you return them from their mission.
I had a level 20 strike team well before this popped for me, however, my 19 team turning level 20, while in single player, gave me the achievement.
I mostly used the game's Multiplayer/Strike Teams/ Missions (saved the last hour of the trial before the app came out, haha) to send strike teams, and as such, my teams have no negatives, despite failing many times. More on that below.
Some notes:
They get XP if they fail, so even when you only have gold available to strike, strike gold! It's a percentile chance, so risk it! More about failure below.
Manage the time! Long mission? Send them over night. Not going anywhere for a while? Do that shorter mission, but remember to resend them!
You can only view traits when a team is not on a mission. Same for strike team equipment.
Multiplayer Equipment, rotated weekly in the store, costs Mission Funds, the same currency for More teams, and, better team equip. Until they patch negative traits, I'd suggest saving some Mission Funds for Equipment, due to rotation schedules, and focus on two teams... so you have a mistake 20 team, like I did haha. If you don't play MP? Keep recruiting, netting you the other team based achievement.
To hit level 20, stay on them, and try to maximize that time. 2 teams is good to focus on, as that should get you to the next strike reset, to start the process all over again.
My friend thinks that failing two missions in a row causes negative traits, but I feel like negative traits are only gained when they fail and you complete their mission in Single Player. Like I said, I have 2 20 teams, no negatives, and my level 6 team also has 0 negatives.
And now that it's on trueachievements, expect a patch haha.