Instructions
Go to Lanayru Province and find Hena's Fishing hole at the top of the river. Go to the northwest corner, past the bridge. Fish here until you find the Sinking Lure, which is critical for catching the Loach.
Leave and return to the fishing hole until you notice that there are green leaves on the trees. This means it's summer, which is the best time to catch the loach. Note that you don't have to wait for seasons to change, every time you leave and return to the fishing hole, the season will change.
Go to the northernmost area of the fishing hole, the cove, and fish for a while until you get the loach. The season makes it extremely likely that it will appear and the sinking lure makes it much easier to catch. When you catch the fish, Hena will put your picture up in the fishing shack.