Every time you press the plus button, you get 6 buildings.
The key to getting this achievement, then, is to completely empty your inventory of buildings every single time. Don't leave any lying around. Only when your inventory is totally devoid of buildings do you press the + button to get more buildings.
While not optimal for racking up the highest possible score, it's not difficult to get to 1,000 points via this method. Just run on the first island until you can go no further, then keep going on the second island. The achievement will pop when you cross 1,000 points without ever having had more than 6 buildings in your inventory.