Here is the full list of all 20 Lost Artifacts: Time Machine achievements.
For constructing a building
For clearing one obstacle
For fixing the portal
For catching the kraken
For the First Sands of Time
For the Second Sands of Time
For getting rid of the Bandit
For speeding up workers
For stopping time
For restoring time altars
For restoring the water mill
For activating the portal
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
For catching 30 mammoths
For catching 30 skeletons