Here is the full list of all 21 Tinkertown achievements.
Craft your first Item
Plant your first seed.
Catch your first Fish.
Catch one of each available Fish.
Craft a Globe.
Enter the Forest Dungeon.
Defeat the Heart of the Forest.
Enter the Desert Dungeon.
Defeat the God of Death.
Enter the Ice Dungeon.
Slay the Shrine Maidens.
Talk to an NPC.
Place any placeable item.
Find every Mine and Dungeon entrance on the Map.
Slay all Dungeon Bosses.
Slayed the first enemy.
Slay every Monster in Tinkertown
Gather all Minerals from Stone to Orichalcum.
Gather all types of wood from Regular Wood to Gray Wood.
Find all NPCs
Crafted all craftable Items.