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.