Starting in 867, choose to start as any ruler, and pick Maharaja Bhoja (Pratihara) in the north of India. Make sure you have ironman turned on to actually unlock achievements.
Go to your council, have your Rajpurohit (religious councilor) fabricate a claim on the county of Kanchipuram (this is the northmost part of the Chola Raj near the southern tip of India). Turn the speed up to 5, and wait for about 3 years to pass. An event should pop up for you to pay for the claim to be created, and you should have more than enough to afford it.
Now just declare war against Chola and march your army south. No matter the amount of attrition, you should have more than enough to win the war, and, in turn, get the last Hindu Holy Site for the achievement. It may take a few minutes, but it should pop once you own the county.