The only way to have another company own property is to build something and then sell it through the Market menu. The challenge here is that the AI will start selling off its assets if it has a lot of one item. As such, the best way to earn this achievement is to build a resource center and separate out the convenience stores into 10x10 blocks. Build ten of those groups of 10x10, then pause the game. Save your game in a new slot as you will want to reload after this done. Go to the Market menu and use to scroll to Property, and use the D-pad to change the sub menu to your stores. Press 1,000 times to sell them to the AI, unpause the game, and the achievement should unlock after about 10 seconds. If it doesn't, this was likely caused by not selling the full 1,000 stores, so pause the game again to prevent the AI from selling anything, sell more of the stores to the AI, and unpause again.
If you are following the road map, you should do this on the first map after clearing the scenario.