Here is the full list of all 45 DPS IDLE achievements.
Open up to 24 continents
Open up to 5 continents
Open up a new continent
Hire 5 heroes
Boil 20 potions
Kill 15 bosses
Join the 5 guilds
Get to the 8 location
Get 50 gold cards
Get 25 gold cards
Hire two heroes
Join the 3 guilds
Get 60 silver card
Boil 5 potions
Get 30 silver card
Boost the card to 7
Kill 5 bosses
Boil potion
Kill 2 bosses
Get to the second location
Get to the 4 location
Get 5000000000000000 poisonous DPS
Kill 10000 monsters
Get 3 gold cards
Get 500000000000000000 DPS
Get 1000000000 poisonous DPS
Get 5000 leafs
Hire one hero
Get 5000000000000000000000000 gold
Enhance the sphere of magic to 31
Boost the card to 4
Get 1000000000 DPS
Boost the card to 2
Get 100000000000 gold
Kill 500 monsters
Get 5000 poisonous DPS
Join the guild
Get 100 leafs
Get 10 leafs
Get a silver card
Get 300 DPS
Get 5000 gold
Enhance the sphere of magic to 6
Kill 10 monsters
Open the sphere of magic