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