Here is the full list of all 30 Doctor Who: The Adventure Games achievements. It takes around 8-10 hours to unlock all of the achievements on Windows.
Found all the Jacobean Facts
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Found all the items in the Drawing Room
Collected all the cards in Episode 1-4
Collected all the Doctor cards
Collected all the Companion cards
Collected all the Jelly Baby cards
Collected all the Enemies cards
Found all the facts in Blood of the Cybermen
Found all the facts in City of the Daleks
Completed all the Episodes of the Adventure Games
Finished the Gunpowder Plot
Discovered what was hiding onboard the Rutan ship
Found the Plotters and Lady Winters secret
Tracked the source of the time lesions
Saved Poseidon base from the Vashta Nerada
Collected all the Freinds cards
Found all the facts in Shadows of the Vashta Nerada
Investigated the source of the trouble
Gained access to Poseidon Base
Defeated the Entity
Reunited the Doctor and Amy
Found all the facts in TARDIS
Rescued the Doctor
Defeated the Cybermen?
Discovered what happened at the GSO base
Rescued Chisholm from the ice
Saved history from the Daleks
Discovered the Dalek plan
Escaped from the ruins of London