River King: Mystic Valley
This game is titled River King: Mystic Valley in North America, Harvest Fishing in Europe, and Kawa no Nushi Tsuri: Komorebi no Tani, Seseragi no Uta in Japan.
Use the stylus to quickly circle the middle of the touchscreen two times. Briefly lift the stylus from the touchscreen, then quickly make two circles again. Repeat this to keep your line below 25% and prevent the fish from going off to the site. You should be able to catch any size fish in less than 30 seconds. If your line tension gets high, try creating one and a half circles (or even less) with the stylus instead. You can also pause slightly longer while the stylus is off the touchscreen.
Strategy guides from GameFAQs