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