The battle against the Angler Fish happens in 2D underwater, where the monkfish will charge against you crashing into the walls, so you will have to remain above it, since its weak point is the light above its head. Then you should take advantage of this, knocking down with your sword to cut, so when the monkfish crashes against the wall pieces of roof can fall. The monkfish will fall to the ground without moving after a few strokes.
In case you hear the Monk screaming, it will mean he is asking for reinforcements. So Mini-Angler Fish will leave the bottom, so you must take out the mini fish with a single sword strike and continue focusing on your goal. Continue hitting him and eventually he will be defeated.
Now that you know how to beat angler fish in Legend of Zelda Link’s Awakening, don't wait any longer and try.