From Nookipedia, the Animal Crossing wiki
The soft-shelled turtle (スッポン, Suppon) is a type of fish that can be found in the river in Animal Crossing: New Leaf. Between August and September, the soft-shelled turtle can be found starting at 4 pm and ending at 9 am.
 Donating in New Leaf
"These relatives of common turtles will not let go when they decide to bite down on something. Although they can be quite shy, they will become a bit aggressive when threatened. They are often found in water and are very good swimmers because of the flat shape of their shells. They swim with their snouts over the surface of the water so they can breathe. Soft-shelled turtles aren't safe to hold because they are so prone to biting at the slightest movement. However, if one bites down on you, it will usually let go when you put it safely back in the water."