Requires an additional controller.
Setup....
-Select Play > Multiplayer from the main menu, then offline.
-Choose to Affection 2 player map.
-Change the game mode to elimination
-Change your race to Robot
-Select any tech that you have (as you level up and unlock more advanced tech then these can speed up the process) - Selecting tech that improves your population growth and ship speed are advised once you unlock them
-Join the game with the second controller and change the enemy race to Human (this way they never have more than 40 population)
Once the game begins, Press X on your home planet then upgrade your planet twice, wait until you are at max population (I was safely attacking once I had 85) and just go attack the enemy planet with everything you have. Game won! The enemy never tries to colonise any other planets.
Each game nets you 125xp in about 1:00 minute. It's a little boring but is rather helpful if like me finding the campaign difficult curve a little daunting, as with this method you can unlock more tech earlier which helps along the way for campaign.
Leveling info
LVL - XP requirement (note the XP requirement is reset after every level)
2 - 400xp
3 - 500xp
4 - 600xp
5 - 700xp
6 - 800xp
7 - 900xp
8 - 1000xp
9 - 1100xp
10 - 1200xp
Total xp required = 7800xp = 63 games played
So should take just over an hour to grind this achievement out with the above method excluding menu time.
Note - replaying campaign missions halves the reward and takes longer so I can't find a quicker and easier method than this at the moment.