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