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