EDIT: This list is now updated with the new items introduced in version 1.5 (Spring 2021), making the whole list spill over on to a third page. All of these items appear to be necessary to earn the achievement, now.
The other solution is no longer complete -- at some point between December of 2016 (that solution) and January of 2020 (this posting), some items have been added to the achievement. Here's the current list, by row, from the in-game "Collections" list (found by
then
5 times to "Collections" tab):
Page 1: Wild Horseradish -- foraged in Spring
Daffodil -- foraged in Spring
Leek -- foraged in Spring
Dandelion -- foraged in Spring
Parsnip -- grown in Spring
Cave Carrot -- found frequently in The Mines
Coconut -- foraged in The Desert, after Bus is 'repaired'
Cactus Fruit -- foraged in The Desert, after Bus is 'repaired'
Banana -- banana sapling may be purchased from Ginger Island trader, earned from Professor Snail, or found inside Golden Coconut
Sap -- chop down any tree
Large Egg (white) -- buy chicken from Marnie for your coop, hope for yellow chick
Egg (white) -- buy chicken from Marnie for your coop, hope for yellow chick
Egg (brown) -- buy chicken from Marnie for your coop, hope for brown chick
Large Egg (brown) -- buy chicken from Marnie for your coop, hope for brown chick
Milk -- buy cow from Marnie for your barn
Large Milk -- buy cow from Marnie for your barn
Green Bean -- grown in Spring
Cauliflower -- grown in Spring
Potato -- grown in Spring
Garlic -- grown in Spring
Kale -- grown in Spring
Rhubarb -- grown in Spring, seeds bought from Sandy, at "Oasis"
Melon -- grown in Summer
Tomato -- grown in Summer
Morel -- choose 'Mushrooms' instead of 'Fruit Bats' with Demetrius
Blueberry -- grown in Summer
Fiddlehead Fern -- foraged in Summer in 'Secret Woods'
Hot Pepper -- grown in Summer
Wheat -- grown in Summer or Fall
Radish -- grown in Summer
Red Cabbage -- grown in Summer
Starfruit -- grown in Summer, seeds bought from Sandy, at "Oasis"
Corn -- grown in Summer or Fall
Unmilled Rice -- grown in Spring
Eggplant -- grown in Fall
Artichoke -- grown in Fall
Pumpkin -- grown in Fall
Bok Choy -- grown in Fall
Yam -- grown in Fall
Chanterelle -- choose 'Mushrooms' instead of 'Fruit Bats' with Demetrius
Cranberries -- grown in Fall
Holly -- foraged in Winter
Beet -- grown in Fall, seeds bought from Sandy, at "Oasis"
Ostrich Egg -- solve Journal Scrap #10 on Ginger Island
Salmonberry -- foraged in Spring (days 15-18)
Amaranth -- grown in Fall
Pale Ale -- ferment hops (grown in Summer) in a Keg
Hops -- grown in Summer
Void Egg -- buy egg from Krobus, if you haven't gotten one otherwise
Mayonnaise -- put white or brown egg in Mayonnaise Machine
Duck Mayonnaise -- put duck egg in Mayonnaise Machine
Void Mayonnaise -- put void egg in Mayonnaise Machine
Clay -- hoe your land
Copper Bar -- smelt 5 copper ore in a furnace
Iron Bar -- smelt 5 iron ore in a furnace
Gold Bar -- smelt 5 gold ore in a furnace
Iridium Bar -- smelt 5 iridium ore in a furnace
Refined Quartz -- smelt broken CD or broken glasses in a Recycler
Honey -- any flavor of honey, made in a Bee House
Pickles -- any flavor of pickle, made by any vegetable in a Preserves Jar
Jelly -- any flavor of jelly, made by any fruit in a Preserves Jar
Beer -- ferment wheat (grown in Summer or Fall) in a Keg
Wine -- any flavor of wine, made by fermenting any fruit in a Keg
Juice -- any flavor of juice, made by pressing any vegetable (except Hops, Wheat) in a Keg
Clam -- foraged on The Beach
Poppy -- grown in Summer
Copper Ore -- found in The Mines
Iron Ore -- found in The Mines
Coal -- found in The Mines
Gold Ore -- found in The Mines
Page 2: Iridium Ore -- found in Skull Cavern
Wood -- chop down any tree
Stone -- pickaxe any small stone on your farm
Nautilus Shell -- foraged on The Beach in Winter
Coral -- foraged on The Beach
Rainbow Shell -- foraged on The Beach in Summer
Spice Berry -- foraged in Summer
Sea Urchin -- foraged on The Beach
Grape -- foraged in Summer, grown in Fall
Spring Onion -- foraged in Spring
Strawberry -- grown in Spring, seeds bought at Egg Festival (Spring day-13)
Sweet Pea -- foraged in Summer
Common Mushroom -- choose 'Mushrooms' instead of 'Fruit Bats' with Demetrius
Wild Plum -- foraged in Fall
Hazelnut -- foraged in Fall
Blackberry -- foraged in Fall
Winter Root -- hoe the 'Artifact Spots' in Winter
Crystal Fruit -- foraged in Winter
Snow Yam -- hoe the 'Artifact Spots' in Winter
Sweet Gem Berry -- grown in Fall, seeds bought from Traveling Cart
Crocus -- foraged in Winter
Red Mushroom -- choose 'Mushrooms' instead of 'Fruit Bats' with Demetrius
Sunflower -- grown in Summer or Fall
Purple Mushroom -- choose 'Mushrooms' instead of 'Fruit Bats' with Demetrius
Cheese -- put cow's milk in a Cheese Press
Goat Cheese -- put goat's milk in a Cheese Press
Cloth -- put wool in a Loom
Truffle -- buy a pig from Marnie, open the barn door, pig eventually finds
Truffle Oil -- put a truffle in an Oil Maker
Coffee Bean -- frequently sold at Traveling Cart
Goat Milk -- buy goat from Marnie for your Barn
L. Goat Milk -- buy goat from Marnie for your Barn
Wool -- buy sheep or rabbit from Marnie for your Barn or Coop
Duck Egg -- buy duck from Marnie for your Coop
Duck Feather -- buy duck from Marnie for your Coop
Caviar -- stock Fish Pond with caught Sturgeon fish, put Sturgeon Roe in Preserves Jar
Rabbit's Foot -- buy rabbit from Marnie for your Coop
Aged Roe -- stock Fish Pond with Carp or Herring (or others), put produced Roe in Preserves Jar
Ancient Fruit -- grown in Spring, Summer, and Fall; donate Ancient Seed Artifact to get seeds
Mead -- ferment any Honey in a Keg
Tulip -- grown in Spring
Summer Spangle -- grown in Summer
Fairy Rose -- grown in Fall
Blue Jazz -- grown in Spring
Apple -- tree grows fruit in Fall
Green Tea -- brew Tea Leaf in a Keg
Apricot -- tree grows fruit in Spring
Orange -- tree grows fruit in Summer
Peach -- tree grows fruit in Summer
Pomegranate -- tree grows fruit in Fall
Cherry -- tree grows fruit in Spring
Bug Meat -- kill any flies or bugs in The Mines
Hardwood -- upgrade your Axe, chop larger wood blockage on your farm
Maple Syrup -- craft a Tapper, put on Maple Tree
Oak Resin -- craft a Tapper, put on Oak Tree
Pine Tar -- craft a Tapper, put on Pine Tree
Slime -- kill most any Slime in The Mines
Bat Wing -- kill any Bat in The Mines
Solar Essence -- kill any Ghost, Metal Head, or Squid Kid in The Mines
Void Essence --kill any Shadow Brute or Shadow Shaman in The Mines
Fiber -- scythe the weeds on your farm
Battery Pack -- place a crafted Lightning Rod on your farm, wait for storm
Dinosaur Mayonnaise -- incubate the FIRST Dinosaur Egg you find in your Coop, put an ensuing Dinosaur Egg in the Mayonnaise Machine
Roe -- stock Fish Pond with Carp or Herring (or others)
Squid Ink -- stock Fish Pond with Squid or Midnight Squid
Tea Leaves -- visit Caroline's Sun Room (past Kitchen) between 9am-5pm to initiate Tea options
Ginger -- found growing in many locales on Ginger Island
Taro Root -- kill Magma Duggies in the Volcano Dungeon, plant a Taro Tuber
Pineapple -- kill Hot Heads in the Volcano Dungeon, plant a pineapple seed
Mango -- kill slimes in the Volcano Dungeon, eventually acquire Mango Sapling
Page 3:Cinder Shard -- kill Magma Sprites in early levels of Volcano Dungeon
Magma Cap -- found growing in Volcano Dungeon
Bone Fragment -- easiest may be to kill Skeletons in The Mines (lvl 71-79)
Radioactive Ore -- find Qi on Ginger Island, perform Danger In The Deep quest
Radioactive Bar -- smelt Radioactive Ore