Prerequisite: Check your mail box on the 8th day
Reward: Diving Suit
Unlocks: Explore the Ocean, 22 meters
Farming is far from the only thing you can do in Coral Island, and not long after starting a new game you'll be hit with a barrage of options for occupying your time. Diving is one of them, and so long as you keep checking your mail box - for me the letter arrived on the eighth day - you'll eventually trigger Into the Ocean.
Into the Ocean steers you towards the diving pier. Head east out of your farm until you see a big, stone sign on the outskirts of town. Head south of here, past another sign, until you reach a boardwalk. The Coral Inn is on your left. Keep going south and you'll hit a cut scene with Ling, a researcher, who bemoans the polluting of the water. She needs someone to help her curtail the effects of the pollutants, and gives you a Diving Suit to help out.
South of where you met Ling you'll see a boat. Approach it and you can start diving.
Diving
Diving operates more or less the same as moving around on land, only you're swimming. You can stop diving at any time by approaching the anchor of your boat, and you can reposition the anchor with the stroke of a key. (On PC at the moment it's the X key.) While underwater you can use your Scythe to destroy heaps of garbage, within which you'll find crafting materials, as well as the occasional treat, such as an Ornate Coffer.
Your mission here is to activate five Solar Orbs. The Solar Orbs are trapped beneath heaps of trash, and when dug up they will trigger a nearby pillar, clearing the immediate area of pollution. This will allow you to explore more areas where you can find other Solar Orbs. A path of light will meander from the Solar Orb to a second pillar, and any trash in the way will stop the light, so you may need to do additional trash cleanup before you can cleanse the area fully.
The Solar Orbs don't appear under the same pieces of trash any two times, so this guide can't provide exact directions. Sometimes they'll appear near their respective pillars, whereas sometimes you won't even be able to see the pillar on the screen anymore when you finally locate the Solar Orb. You just need to keep slashing trash out of your way until you find them.
There are more than five pillars that you can find by exploring, but you only need to activate five Solar Orbs and cleanse coral in five places to satisfy the requirements of the quest. (Though keep this activity in mind, as it will allow you to explore deeper in this area if you wish to come diving again.) Activating even five pillars takes a while, so either bring consumables to restore your Stamina - you'll need to leave the water to eat them, mind - or come back several days in a row.
Leave the water once you've activated five Solar Orbs and head to town. Ling's Lab, your next destination, is located a short trip east of the Community Center. It's open 8:00 to 17:00 (8:00 to 15:00 on Fridays), every day but Saturday. Ling will explore more of the situation in the ocean, and give you the task of continuing to clean the depths. This will unlock a new quest for you, Explore the Ocean, which will have you activating more Solar Orbs.
Explore the Ocean
Explore the Ocean is more or less an expanded version of Into the Ocean. The primary difference is that you now need to clean up 20 oil patches, in addition to the five you've already cleared. This requires activating 15 more Solar Orbs, which, unsurprisingly, can take quite a while. You'll need to explore a significant chunk of the seas to trigger 15 more Solar Orbs.
As you explore you'll wind up running into some turtles that bar your path. These turtles want produce - helpfully displayed in dialogue windows - before they will move out of your way. You'll need to give them one piece of produce of the desired level of quality to get rid of the turtles. Use Fertilizer to maximize your chances of growing high-quality produce. The produce the turtles want changes from season to season, ensuring that you'll never need to wait an entire year for a particular fruit or vegetable to come back into season.
Given the size of the diving area - and the lack of an in-game map - it's very easy to get lost while trying to find all 20 Solar Orbs. I recommend using this map to navigate until something better is implemented in-game.
