This Achievement is glitchy.
I won as Defender but read somewhere that it will glitch if you win as Defender. Then I tried again and won as Attacker and it still hasn't unlocked:
Sorry, this Game Clip has been removed
It's not stuck in the "Xbox Achievement Unlocking..." thing that happens sometimes and then will unlock a few days later. It just says it's still locked. I hear an achievement sound at the end but I don't know if that's related or if it's some other notification.
EDIT: I re-installed the game and restarted my console. My Xbox still said it wasn't unlocked, I won a few games against AI and PvP and now I unlocked it with a timestamp of 6 hours ago. I won my first Breach Match closer to 12 hours ago. So... I have no idea what happened but that's what I did to finally unlock it.