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