Dolphins are predators and they usually eat fish. This is what they are given when you see them participating in dolphin shows -- they are fed fish out of a bucket. Of course, they do not hunt down big sharks but eat fish the size they can handle without having to bite off chunks of it. Dolphins do not bite but swallow. If a fish is too big to fit in their mouth, they generally speaking do not eat it.
Dolphins also eat squid. I am sure they would eat rodents but those are not found in the sea. So they are restricted to whatever they can find in their natural habitat.