Here is the full list of all 21 Sword of Atlas achievements.
Pick up the Sword in the Tutorial
Chase the enemy captain out of Chapter 1
Free either the mage or the hunter from the cage in Chapter 2
Defeat the enemy captain in Chapter 3
Stop the ritual in the forest in Chapter 4
Discover the ancient secret in Chapter 5
Visit the summer chateau in Chapter 6
Defeat the boss in Chapter 8
Beat game using Active ATB Mode
Flee to the airship in Chapter 6 in under 1:00
Complete any level with only one hero remaining
Reach Max Hero Level
Beat Chapter 7 and 8 without an Eyestalk exploding
Beat Chapter 8 without getting hit by Eye of the Father attack
Try to sneak past the guards in Chapter 2
Cross the river in Chapter 1 twice before choosing a companion
Destroy all 4 benches in the Tutorial
Trigger the bard's amphitheater solo in Chapter 6
Walk through the sludge in Chapter 5
Strike the killing blow in Chapter 8 with the bard
Collect all achievements