Here is the full list of all 30 On My Own achievements.
Travel to a different camp
Catch 5 animals in snares or traps
Travel to the winter world
Craft a bundle bow
Craft an item to aid in survival
Start a fire to stay warm during the night
Forge food from an edible plant
Chop down a tree
Find a secret letter
Equip a fox skin hat
Chop 200 trees down
Kill 5 animals with a bow
Kill 5 foxes
Catch 5 Fish
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
Encounter/survive an avalanche