You can comfortably work on this Trophy in the main campaign by doing every major and minor operation. That way you should get to Rank 10 during the final mission.
You can also get this if you have the Hangar 6 R&D dlc. The dlc campaign will get you to Rank 10 if you want it or not. The rank system works a bit different here. You don't get XP for killing aliens. You will level up after every mission when you speak to Dr. Dresner.
The dlc way is a lot faster but both work of course