From Nookipedia, the Animal Crossing wiki
The Tuna (マグロ, Maguro) is a rare fish that can be found in the ocean all day between November and March. The fish sells for an expensive 7,000 Bells at Tom Nook's store. The fish has a huge shadow size.
Donation to the museum
In Wild World
Blathers will say this when the Tuna is donated to the museum: "If a tuna stops swimming, it will stop breathing and expire, eh wot? As you can imagine, this means that it must swim when it sleeps as well. I think every day about how marvelous life would be if I could work in my sleep!" One can find the Tuna in the back tank with the other ocean fish.
In City Folk
Upon being donated to the museum, the Tuna can be found in the back tank with other ocean fish. When given the fish, Blathers will say this: "If tuna stop swimming, they actually lose the ability to breathe and can perish! ...Which means that even while resting, this fish just keeps swimming, eh wot? I really prefer to focus on resting up rather than napping... Rather lucky I was born an owl, wot wot!"
In New Leaf
The information board in front of the tank that holds the Tuna says the following:
There are various types of tuna in existence. The type of tuna that appears in Animal Crossing series appears to be a Northern bluefin tuna, judging by the overall shape and coloration of the body. As a result of its uses, it has become overfished, and because of its late maturity, it is increasingly difficult for it to reproduce to sustain the demand. It preys on squid, crustaceans, horse mackerel, sardines, and herring.