Edit: It has come to my attention that a patch has/will disable this method. If so please let me know. I do not know of any other methods to speed this up.
You should have no trouble getting this achievement by simply playing through the game.
The quickest way to level up the Inquisition to rank 10 is by buying treaties from Farris in Skyhold. He is unlocked by completing the war table mission Power for a Price* and you can then find him by the other merchants near Blackwall. After you purchase the treaties you can immediately sell them back. This way you earn the power and influence and you don't lose any money. You can keep doing this to speed up the following achievement as well:
*Thanks to SilasCova