Here is the full list of all 27 Gnomes Garden Lost King achievements.
For building a flying house
For completing all levels with 3 stars
For building your seventh pigeon house
For building your sixth pigeon house
For catching a mound
For building the great portal
For activating an altar
For building your fifth pigeon house
For exterminating Rats
For restoring a ship
For building your fourth pigeon house
For building your third pigeon house
For growing waterlillies
For completing 15 levels with 3 stars
For speeding up construction
For catching sheep
For speeding up workers
For building your second pigeon house
For building your first pigeon house
For clearing thorns
For completing 5 levels with 3 stars
For finding hidden animals
For constructing a building
For restoring a farm
For clearing one roadblock
For collecting all trophies
For stopping time