I heard recently that soda can rob calcium from your bones. I've also heard that soda is actually dehydrating. And if he is drinking multiple diet pepsis with caffeine, this can increase his risk of hypertension.
Sugar can lead to plaque formation in blood vessels, but diet pepsi has aspartame. Your boyfriend should be looking at his intake of saturated fats, trans fats, partially & fully hydrogenated oils and sugar and trying to cut those things way down. Also, he will want to increase his exercise (if he's not getting enough) to try to bring up his HDL, which is supposed to fight the bad LDL.
Some people naturally have higher levels of cholesterol- it can be hereditary, where their own bodies make large amounts of it. He'll want to talk to his doctor if diet and exercise are not bringing his LDL in check.
Diet pepsi does not contain cholesterol so from that standpoint it wouldn't be harmful.
But excessive drinking of Pepsi can erode tooth enamel. Diet Pepsi does not contain ascorbic acid or erythorbic acid so there may not be dental risk.