For the standard approach, there's kind of a minigame going on. If the fish wiggles around, stop reeling it in because that will deplete your stamina ultra fast. Only reel when the fish is calm.

I'd reccomend the nihilistic approach tho.
Catch the biggest fish by not trying to catch them.
Cast close to the shore and if a fish gets hooked, do nothing. Only slowly walk away from the shore. You can pull the fish on land that way without losing stamina, even high tier ones.
You can simply pick the fish up once they "followed" you to the shore.