To get the Hylian Loach easier, try searching for the "sinking lure." It's most likely at the rocks to where the stream flows or the crack in the wall to where the water is excreting outward. If it's not there, check the long grass. As a last resort, check the middle of the lake. It's a tedious task, but it'll make things easier. What the sinking lure does is that instead of the lure you get from the counter that merely floats, the sinking lure can let you catch a fish any time you wish. For a fish to bite on the floating lure, you would have to wait until it gets hungry and starts jumping atop the surface. However, the sinking lure let's you sidestep the disadvantages. Keep in mind that other fish may bite on the rod before the Hylian Loach does.
Note: (If you talk to the fisherman enough times by saying "Let's talk about something else", the sinking lure can become legalized)
The Hylian Loach should be around the right side of the pond (a.k.a. from the stump in the lake perspective). The best way to search for this is to equip the Iron Boots and Zora Tunic to manually search for it. If it's not there, you may need to come back. Keep in mind it resembles an eel. After you somehow manage to grab ahold of it, immediately set your hook, and put your fishing skills to the test. Try not to put too much stress on the lure by not reeling it in fast all the time. Try to never fight the fish, in fact, try to pull the line to where the fish is swimming to turn the momentum to your advantage. You'll know it's the Hylian Loach when the Fisherman identifies it, and estimates about 36 pounds. Congratulate yourself, as although in a broad view it's miniscule, it establishes an inspiration of confidence of your skills forming one of the hidden tasks of the game.