It does not take an elephant rifle to take down hippos, but they are big, tough animals. You want something with a lot of penetration.
Most would say a .375 H&H or above. The .375 is the minimum legal caliber to hunt hippos in South Africa.
Lots of hippos have been taken down with .308/.30-06/.303 loads or less.
If I were hunting hippos, I would likely opt for a .375.