Update December 2021 - Thank you XI AlphaMale IX for the update, From the devs:
The current way to complete these achievements is to complete a certain number of adventures, but we left the wording vague on how many in case things change in the future. Right now, Doer of Deeds requires completing 6 adventures, and Great Deeds requires 10.
Update Aug 2020 - Thanks Chui for the update:
There was an issue with the way Doer of Deeds and Great Deeds were updated, that has now been resolved. They should complete based off of story milestones that roughly corresponded to the original Deeds system on log in. Doer of Deeds will complete based on the quest Back Up from Ebon Downs. Great Deeds will complete based on the quest Protector's Emissary.
Update July 2020 - Thanks YODA12320 for the link to the Developer blog:
'The in-game achievements that require Deeds can once again be achieved. Their descriptions have been updated to match the requirements.'
Update June 2019 - Since the most recent update, Mod 16, the deeds are no longer in the campaign journal, the related quests are still available but testing is needed to see when the related journal achievement unlocks, hopefully this still unlocks the achievement. Anyone with info please comment below.
In the Campaign list (under Quests) all the different quest areas are listed, working through these will earn you deeds. There are 17 areas for one character to complete (this does not include the level 70+ campaigns as they do not state 'deed' so unless confirmed otherwise I believe these are not included).
I have listed them below in order as they can be accessed by playing through the quests from Sergeant Knox, you can earn 11 for this achievement with one character:
Sleeping Dragon Bridge
Return of the crown
Tower District
The Plague Tower
Blackdagger Ruins
Neverdeath
Helm's Hold
Ebon Downs
Vellosk
Pirates Skyhold
Icespire Peak
Chasm
Rothe Valley
Mount Hotenow
Whispering Caverns
Hero of Neverwinter
Protector's Emissary
Once you have completed an area you will be able to claim the deed, each area deed under the campaigns list shows you the required quests in order to complete them, they also appear in your journal.
If you have already completed the areas but not logged in since Benign Order of the Third Eye quests were added (around Jul/Aug16 sometime) then the deeds will be available for you to claim.