The boat, owned by Dolphin Spotting Boat Trips, was carrying 12 passengers on a private dolphin spotting trip.
They had spotted a few dolphins in the water, including Ghost, who is a favourite with dolphin spotters.
Sarah Michelle Wyer, 30, the company's photographer, said: "It was an incredibly rare encounter where a pod of bottlenose dolphin attacked and killed a common dolphin calf.
"I've never seen that behaviour before. It's very common for bottlenose dolphins to attack porpoises but not a common dolphin calf."
Holly Williams, 35, was one of the passengers on the boat and said: "They started jumping out the water. We thought they were just playing."
The group saw something being flung out of the water by the dolphins and initially thought it was a salmon, but they realised it was a common dolphin calf.
Dylan Coundley-Hughes, 22, is a researcher for the SeaWatch Foundation caught the attack on camera.
"These kind of attacks are so rare to see in person. We know they happen in the wild but it's rare they're ever seen," he said.
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