Here is the full list of all 116 Tap Adventure: Time Travel achievements.
Complete first Quest
Hire 3 heroes
Receive 1 000 of damage in total
Level up hero
Kill 10 bosses
Open first chest
Open boosted chest
Hire 2 heroes
Deal 1000 damage with Magic
Kill an enemy with magic
KIll first boss
Receive gift from Fay
Hire first hero
Obtain Hero Ring
Visit 3 new locations
Visit 5 new locations
Visit 7 new locations
Visit Crossroads once
Visit Crossroads 100 times
Reach 100th stage
Reach 500th stage
Reach 1000th stage
Reach 1500th stage
Reach 2000th stage
Reach 2500th stage
Reach 3000th stage
Hire 4 heroes
Hire 5 heroes
Hire 6 heroes
Hire 7 heroes
Collect all Hero Rings
Max Hero Ring
Reroll artifact
Demolish artifact
Chronosphere bought
Maxed Chronosphere
Collect 5000 Arrowheads
Collect 1000 Fingers
Collect 1000 Bones
Collect 1000 Horns
Collect 1000 Eyeballs
Found first dropable artifact
Craft new artifact
Craft 5 artifacts
Craft 15 artifacts
Upgrade Magic to lvl 100
Upgrade Magic to lvl 500
Upgrade Magic to lvl 1000
Upgrade Magic to lvl 2000
Upgrade Magic to lvl 3000
Create first Time Loop
Create 10 Time Loops
Create 25 Time Loops
Create 100 Time Loops
Create 1000 Time Loops
Open 10 chests
Open 100 chests
Open 250 chests
Open 1000 chests
Receive 25 gifts from Fay
Receive 100 gifts from Fay
Boost chest
Open 10 boosted chests
Open 100 boosted chests
Enchant Mimic
Enchant 10 Mimics
Enchant 100 Mimics
Upgrade Mimic to lvl 5
Build at least 1 organelle of each type
Max all organelles for Mimic
Open Mimic chest
Collect Fayball from Mimic chest
Collect Hero Ring from Mimic chest
Collect Random Gift from Mimic chest
Collect 10 of Wizard Notes
Collect 10 Gratogmorres
Collect 10 Tomes of Shield
Summon friend's Fay for help
Kill 100 bosses
Kill 1000 bosses
Kill 3000 bosses
Kill 10000 bosses
Receive 100 000 of damage in total
Receive 10 000 000 of damage in total
Receive 10 000 000 000 000 of damage in total
Deal 100 000 damage with Magic
Deal 10 000 000 damage with Magic
Deal 10 000 000 000 000 damage with Magic
Level up hero to the max
Level up 2 heroes to the max
Level up 3 heroes to the max
Level up 4 heroes to the max
Level up 5 heroes to the max
Level up 7 heroes to the max
Level up all heroes to the max
Encounter with the Governor's Club
Collect 100 gems from Quests
Spend 50 manacoins
Spend 250 manacoins
Spend 999 manacoins
Collect 100 manacoins
Collect 250 manacoins
Collect 500 manacoins
Use active skill
Use active ability of each hero at least one time
Use active skills 100 times
Level up passive skill to the max
Collect 100 runestones
Collect 1 000 runestones
Collect 20 000 runestones
Hire full team of imp-workers
Hire 100 imp-workers in total
Hurry up imp-workers 100 times
Complete 10 Quests
Complete 100 Quests