(version as of writing: 1.2.1)
Fishing is sort of an annoying minigame until you get the hang of it.
To fish in the game, you'll need the Angler life that gets unlocked part of the way through the main story. Then for the actual minigame...
On land, you go up to a fish and see if the speech bubble with the fishing prompt appears.
You press that button (A for me) and you'll cast your line into the body of water.
The fish will nibble the line and your controller will buzz a bit. Wait until the double red !! marks appear. Then you press that button and you're in the fishing minigame.
The minigame is a stationery version of all of the other gathering. You "move" by rotating your left thumb stick and it'll move around your cursor. The middle is where the fish is and your arrow is the direction you want to pull.
You can peek like the other gathering minigames to see if you can find the sweet spot with the Y button.
The small triple dot bubble means that the sweet spot is in the opposite direction so go a full 180 degrees.
Sweet spot will be the double !! marks
Do your fancy fishing moves and you'll get it.
Both the fish and your rod will have health bars.
The trick I found with this is to use the half-circle trick. It might sound dumb but here's how it works: