Higher tier fishes (or even big lower tier fishes) do require a LOT of stamina.

In order to ensure a catch, eat 3 stamina foods so you have 200-250 stamina, use a boat to go near the fishes, and cast your line 2-3 meters from it. The closer you are, the less stamina will be required. Remember to spam E to pick up the fish as early as possible before it can swim away.