Here is the full list of all 32 Factory Town achievements.
Upgrade Base to level 10
Complete Campaign Map 8
Complete Campaign Map 7
Create 1 Fire Ring
Create 1 Water Ring
Create 1 Crown
Create 1 Necklace
Create 1 Elixir
Create 1 Magic Cloak
Craft 1 Omnistone
Complete Campaign Map 6
Create 1 Air Crystal
Create 1 Water Crystal
Complete Campaign Map 5
Complete Campaign Map 4
Complete Campaign Map 3
Complete Campaign Map 2
Complete Campaign Map 1
Craft 1 Fire Crystal
Create 1 Earth Crystal
Create 1 Fish Stew
Earn 1 Purple Coin
Create 1 Berry Cake
Create 1 Mana Crystal
Create 1 Warm Coat
Earn 1 Blue Coin
Complete any Research
Create 1 Veggie Stew
Create 1 Meat Stew
Create 1 Iron Plate
Earn 1 Red Coin
Earn 1 Yellow Coin