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