To get this achievement you could do two things. Try searching a 1v1 with a buddy at the same time. Use the chat thing to say when you are about to start searching. However, there is quite a slim chance that you will be matched up.
The other way could be to do a 1v1 but search normally. Then ask the opponent through in-game chat if they want to do annihilate rather than do normal vic-points. If the other opponent agrees then you are away, you just need to win the game then. If the other player is a bit stubborn then try tempt them with the fact that there are greater experience rewards at the end. Even if you lose! You do sometimes get people that completely refuse though, so just play a normal vic-point game and try again with another opponent. However, there is the risk that the other opponent might want to cut their losses and just concede before you destroy their base. Try convincing them not to do this, all depends on the personality of your opponent of course :/
You can always team up with buddies and do larger games like 2v2's and 3v3's but then you have to convince 3 opponents to do annihilate and not concede so your chances are a lot lower obviously :(
I personally got this achieve through a 1v1 and asked nicely if they wanted to do an annihilate instead. I was lucky and managed to get it first time because he was a nice guy but you might have to try a bit longer, but don't be disheartened! Keep trying and you will get there! :D