There may not be many side-quests, but they’re all good ’uns. Here’s how you smash them into a solved pulp:

Fishing Rod
Travel to Bannan Island and talk to the Wayfarer in his hut - turns out he’s got a thing for mermaids. To find the ‘mermaid,' leave the hut and kill all the monsters on the western half of the isle. Head towards your boat and the mermaid will be in the water. Hit her with the boomerang and return to the Wayfarer. Huh? No mermaid? Go and talk to Linebeck and return to the Wayfarer again. He’ll give you the fishing rod.

Fishing Quest
Get the rod, as outlined above. Leave Bannan Island and make your way to the fish shadow for some rod training. Keep fishing until you hook a ‘Loovar’ - you may have to move between sea quadrants to get it to randomly appear. Show the Loovar to the Wayfarer back on Bannan. He’ll give you the big fish lure and ask to see any exotic fish you catch with it. You’re after the big daddies - the rusty swordfish and Neptoona, king of fish. Both will appear as swordfish shadows, but Neptoona can’t be caught until you’ve nabbed the swordfish. Show the Wayfarer the swordfish and he’ll send you out for Neptoona. Neptoona appears randomly at swordfish locations. Persevere and you’ll catch him. Show him to the Wayfarer and you’ll get a… heart container. Gee, thanks. 

Link’s Trading Adventure
Visit the traveler’s ship in the NE sea quadrant. Defeat the monsters there and ‘The man of smiles’ will give you the ‘Hero’s new clothes.' Travel to the Link-aping wannabe hero in the NW sea quadrant and give him the clothes. He’ll give you a telescope. Go to the boat in the SE sea quadrant and talk to the guy who’s missing a telescope. He’ll give you the guard’s notebook. Travel to the SW sea quadrant and talk to the traveler that you rescued earlier. Give him his book and he’ll give you his wooden heart. You must have completed the fishing rod side quest to continue. Return to Bannan Island and you’ll find the Wayfarer missing. He’s in the SE sea quadrant, in the western boat of the two. Give him the wooden heart and he’ll tell you to meet him on Bannan. Sail back to Bannan, fighting a sea monster to dock - the same monster that you fought outside Molida island. Enter the Wayfarer’s hut and he’ll give you the swordsman’s scroll. You will now have an ace super spin attack.