Here is the full list of all 23 Lost Artifacts: Golden Island achievements.
For clearing one roadblock
For restoring a plant
For constructing a building
For summoning the tortoise
For the First Fountain
For the Second Fountain
For the Third Fountain
For the Fourth Fountain
For the Fifth Fountain
For the Sixth Fountain
For Seventh Fountain
For getting rid of the Wicked Thief
For speeding up the atlanteans
For stopping time
For restoring the mechanisms
For restoring the water wheel
For activating an altar
For speeding up construction
For defeating the Villain
For completing 5 levels with 3 stars
For completing 15 levels with 3 stars
For completing all levels with 3 stars
For collecting all trophies