Here is the full list of all 20 Lost Artifacts: Time Machine achievements.
For defeating the Villain
For completing 15 levels with 3 stars
For catching the kraken
For catching 30 mammoths
For catching 30 skeletons
For completing 5 levels with 3 stars
For restoring the water mill
For stopping time
For getting rid of the Bandit
For activating the portal
For speeding up construction
For restoring time altars
For the Second Sands of Time
For speeding up workers
For fixing the portal
For the First Sands of Time
For constructing a building
For clearing one obstacle
For completing all levels with 3 stars
For collecting all trophies