This can be easily done by not using cover based pins obviously. Cover based pins are indicated by the barricade icon in the top right corner of the pin when you are choosing your squad in the pin menu. You can have them in your squad when in a match, just don't put it out on play. According to User wizzardSS, as long as you have no covers captured by the end of the match, you are good to go. Once you win the match, the achievement will pop shortly after.
Pins I used included turrets, frags, Reyna Diaz, Kait Diaz, the Shephards and the Butcher mainly and rotated those out. It would be easy as you upgrade ones and use ones you are good with.
User Drazer76 has pointed out that you can also attempt this in Horde mode.
Doesn’t matter if your partner takes cover, as long as you don’t.
I just got it by using assault on enemy while partner moved up the field.
However, others have said it hasn't worked for them even when they dont use cover based troops and their partner does so you may have different results.