I just killed enough sharks to earn a diving helmet and plenty of fins. It took somewhere under two in-game days (48 minutes), and over half of that time was spent waiting. Didn't bother with potions or water candles, used just ordinary pre-hardmode equipment.
Near as I can tell, in normal circ*mstances hostile mobs won't come after you if they can't find a path to reach you. Sharks might have spawned all around you but never come near enough to see, because you're walled safely off from them.
I recommend getting where they have a chance to have a go at you. Assuming you haven't any underwater gear yet, build one ore more "diving bells" in the ocean. Each bell is an upside-down U shape made of some kind of blocks, with the water removed using buckets/sponge, and a platform you can stand on. After removing the water you hop up into the now air-filled space to breathe, then jump back down into the sea to attract (and fight) enemies.
This one can't be entered from the left. If I wanted to allow that I could rebuild it a little higher off the sea bed.
Here's another that can be entered from either side. It's got two banners (crab and pink jellyfish) hanging from its ceiling. On the right side of the picture you can see the light from a glowstick — toss a few of these around the sea floor to light up the unseen area around you.
Standing on the platforms as shown here, any sharks that spawn just randomly drift around. If I step down and fully in the water, they attack… and soon after they attack, they drop stuff. Nine out of ten safety experts agree that sharks should be careful around sharp blades, but do sharks listen? They do not.
P.S.: In the real world diving bells (click to see Wikipedia) are/were one of the first ways of exploring underwater longer than you could hold your breath. Real ones are mobile, not fixed in place like these. They were attached by cables or chains to a boat overhead.
You can't make an open ("wet") diving bell the way I describe here in our world. Instead of using a bucket to empty the water you'd have to release compressed air up into the bell, under sufficient pressure to force the water out the open bottom of the bell, or just retain the air already in the bell when lowering it into the water.
