You’ll trigger this quest on the 6th of Summer in your second year. Demetrius sends you a letter, asking for a Pufferfish. You’ll have to go fishing to find him one for his research.
This quest is primarily a test of your timing. Pufferfish appear in the ocean - in other words, the area abutting the beach and Willy’s Fishing Shop - but they only show up in the morning and the early afternoon, from roughly 12 am to 2 / 3 pm. It’s not a huge window, and when you finally get a Pufferfish on the line it will give you quite a fight. Some tips:
- Make your way to the beach at the start of the day and start fishing first thing. I don’t know exactly when Pufferfish start to appear (12 is the closest I’ve found to a consistent time), but this will give you plenty of time to get there and get in the fishing groove.
- Have Bait attached to your lure. You’ll bring in fish more quickly.
- Get your Fishing Skill to a decently high level. Five or six should be enough to give you a fair chance against a Pufferfish.
- Have at least the Fiberglass Rod equipped, and ideally the Iridium Rod. Faster, easier fishing. Both of them get unlocked by increasing your Fishing Skill (three for the Fiberglass Rod, six for the Iridium Rod).
- Prepare yourself for lots of quick reeling and dramatic changes in elevation. Pufferfish are all over the place on the meter.
Once you’ve snagged a Pufferfish, take it to Demetrius. He lives at the Carpenter’s Shop, and can be found there most of the day. If he’s not at the Shop he can usually be found either in the park to the west of the Community Center or on the banks of the water near the Mines. He’ll give you 750 gold for your Pufferfish, as well as a bump to affection.