Here is the full list of all 30 On My Own achievements.
Forge food from an edible plant
Start a fire to stay warm during the night
Chop down a tree
Craft an item to aid in survival
Catch 5 animals in snares or traps
Equip a fox skin hat
Chop 200 trees down
Kill 5 animals with a bow
Travel to the winter world
Kill 5 foxes
Catch 5 Fish
Travel to a different camp
Survived a bear attack/encounter
Travel to 3 biomes
Travel to all 4 biomes
Equip Jacket, Hat, and Backpack Upgrade
Create a fire without matches or coals
Complete all journal entries for the Woodland Biome
Complete all journal entries for the Woodland Lake Biome
Complete all journal entries for the Alpine Tundra Biome
Eat every edible food in the game
Craft every item in the game
Survive through all 4 seasons
Reached the summit of the Mountain Biome, completing the game
Equip the bear jacket
Find a secret letter
Encounter/survive an avalanche
Craft a bundle bow