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