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