Slime Rancher

Pink slimes can eat everything so finding 10 different foods is pretty easy. Here is a list of the beginning game food. If I miss any feel free to comment below.

Carrot (found growing right outside the ranch)
Pogofruit (grows on trees near the ranch)
Heart Beet (can be obtained by feeding the Pink Gordo or found later in the game)
Cuberry (Found farther along on square trees or from feeding Gordos)
Hen Hen (Appear in nests near ranch, grow from chicks)
Stony Hen (Appear in nests near the ranch)
Roostro
Elder Hen (When a hen gets old it will automatically become this)

Now at this point I unlocked the achievement even though this doesn't reach 10 different foods. There is a possibility plorts count as types of food in which case feed a pink slime: tabby plort, rock plort, and phosphorus plort. If they dont count then here is the rest of the types of food:

Oca Oca
Silver Parsnip
Odd Onion
Mint Mango
Phase Lemon
Prickle Pear
Briar Hen
Painted Hen
Elder Roostro

Pink slimes have no preference of diet and can eat fruit, vegetables, and meats. There are set foods that can be found in all the different biomes, and they can be found as follows.

First things first, Roostros can appear anywhere that any type of Hen Hen can. Also elder Hens and elder Roostros can occur once they've had a certain amount of chickadoos (Hen Hens need 6 and Roostros need 18)

Dry Reef:
Carrots
Pogofruit
Hen Hen
Cuberry

Indigo Quarry:
Odd Onion
Oca Oca
Heart Beet
Stony Hen

Moss Blanket:
Mint Mango
Briar Hen

Ancient Ruins:
Phase Lemon

Glass Desert:
Painted Hen
Prickle Pear
Silver Parsnip
Gilded Ginger (Very Rare)

That'll be plenty to complete the 10 different foods requirement.

Here's my video for all achievements if you'd prefer. Skip to 3:39 for Omnivorous.