You will most likely get most of the achievements just by following the story. After completing the story, you can continue playing, so no achievements are missable.

For some reason a few collectibles are not marked on the maps, so I marked them myself.
Each island has different fish, crop seeds and spice seeds, which you need to collect.

Stranded Survivor
Survive the shipwreck


Cook
Cook your first Food


Artisan
Craft your first Item


Culinary
Discover your first cooking recipe
Recipes are discovered by mixing and matching ingredients, while doing this, the ingredients are not consumed.

Stew for the Crew
Unlock the Stew for the Crew


Reunion
Reunite the whole Crew


Survival Camp
Build all of the Crew member's shacks


The Right Tools for the Job
Unlock all Tools


Danger Ahead
Complete your first combat encounter


Ancestral Recall
Summon the Ancestor


Ship Ahoy!
Complete the Ship


Cursebreaker
Lift the Curse
⠀
⠀
The End
Complete the Story Questline

Farmhand
Discover all Crop Seeds
Open crates and dig up shining spots.

Gourmet
Discover all Spice Seeds
Found in chests.

Angler
Discover every Fish.


Master Chef
Discover all cooking recipes
Trial and error. Or look up a recipe guide.

Architect
Unlock all structures in your camp by increasing your Crew's Happiness Level and build them

Each crew member has their favorite stew ingredients, which fill up the happiness meter twice as fast, but if you don't have their favorite ingredient, anything else will do. I fed my crew with lots of corn.
Here are their favorites.
Charles: Allspice Powder, Bluefish, White Marlin
Sven: Potato, Onion, Clam
Fiola: Cob of Corn, Tomato, Rice, Eggplant
Logan: Carrot, Pumpkin, Crab
Fritz: Chili Flakes, Mackerel, Flounder
Teresa: Cane Sugar, Seabass
Cecilia: Fresh Thyme, Ginger Root, Lobster
Brenda: Black Pepper, Red Snapper

Well Equipped
Unlock all tool upgrades by increasing your Crew's Happiness Level


Happy Crew
Reach Crew Happiness Level 60


Explorer
Discover the whole Map
To fully explore each island you need to have bridges, ladders and climbing ropes unlocked.

Archivist
Discover all Lore Artifacts
Some artifacts are hidden in caves.

Champion's Genesis is on the Central island and Camp site.
Ancient Prophecy is on the North-Western island.
The World's Shaping is on the South-Western island.
Eternal Champion is on the Southern island.
Captain Barbaross' Logbook, Admiral Kennwalk's Notebook and Commander Davenport's Journal are on the North-Eastern Island.

Treasure Hunter
Find and dig up all buried Golden Tools
As you level up your crew happiness level, you can receive treasure maps from the parrot.
Treasure maps are required for getting the Collector achievement. Here are screenshots with golden tool locations.
Golden Axe
Golden Shovel
Golden Fishing Rod
Golden Bucket
Golden Sword
⠀
⠀
Honorable Warrior
Defeat 100 consecutive waves of easy difficulty enemies in the Ancestor's Trial


Each trial took me around 30 minutes. To make the trials easier, do it during the day, have Teresa's hat perk, and bring some food with you.

Powerful Warrior
Defeat 70 consecutive waves of medium difficulty enemies in the Ancestor's Trial


Legendary Warrior
Defeat 50 consecutive waves of hard difficulty enemies in the Ancestor's Trial


This one was a bit tough, don't be cheap and bring some good food with you.
I wish the game had a dodge or a block, getting stunlocked by red pirates is very frustrating.

Hat Collector
Unlock all Hats by increasing your Crew's Happiness Level and mastering the Ancestor's Trial.
In total there are 8 hats. 5 are unlocked from the crew stew, and the last 3 from trials.

Collector
Discover all Items
The required items are seeds, fish, recipes, artifacts, hats, tools, golden tools and treasure maps from the stew.
You don't actually need all items in the game, for example pearls, tentacles, feathers and worn-out dice are optional.

Thank you for reading. I hope this guide was helpful.