Many have already found solutions for achievement, but details themselves seem to be all over the place. I will confrim my method of earning this achievement, including savegame strategy, as I do NOT think it is bugged.
I have the latest patch (as of the writing of this guide) and alll DLC installed. I did not uninstall the patch, clear cache, or transfer my saves to another Xbox 360 as some other sources have suggested.
As many others have pointed out, I can confirm my opinion that this counts for MAIN character kills only, while the main character is under your direct control. I do not believe that it counts other characters' kills while under your direct control. I also believe that this counts only for ONE playthrough, and not across all playthroughs. Simply put, your character must kill 1,000 darkspawn, by him/herself, in one playhthrough beginning to end.
My process and Savegame strategy:
Begin the final fight for Denerim after the march from Redcliffe. Eliminate Darkspawn at the gates and choose your party. I chose Allistair, Oghren, and Morrigan. I headed first to the Elven Alienage and immediately saved my game (overwriting a savegame previously used by this character.) Begin dialog with the elf, and nearly immediately it will auto-save. I held my party back while I went to work on the darkspwan with my main character.
There are sources that indicate that the quest line, started from the elf before the auto-save, must be completed before darkspawn are counted. I do not know if this is true as I did not test it specifically, but I completed the elf quest by speaking to Shianni at the tree after all darkspawn in the alienage were eliminated. After speaking to Shianni, I saved my game by overwriting a previous save, keeping the original Alienage save intact.
After saving the game, I loaded the AUTOSAVE to continue the Alienage from the beginning since there is no autosave after the darkspawn are eliminated from this area, nor is an autosave kicked off after speaking to Shianni. After eliminating darkspawn, the general, and speaking to Shianni a second time (a second full playthrough of the Elven Alienage from loading the autosave,) I saved the game again by overwriting a different, previous savegame.
By this time, there are four saves that I am keeping track of. As far as I can tell, the actuall savegame number doesn't hold any special meaning, so I'll use it to illustrate. Assume that all 20 slots are in use from previous saves throughout the game:
Elven Alienage (10) -- the end of 2nd playthrough of Alienage
Elven Alienage (9) -- the end of 1st playthrough of Alienage
Auto Save (1) -- the autosave from the beginning of Alienage
Elven Alienage (8) -- the beginning of the 1st Alienage
I simply alternated saves between (9) and (10) above at the end of each run.
Save 8 was never truly needed again, but I kept in in case I needed to go back just before the autosave was kicked off, or if I progressed too far on the bridge to kill darkspawn which would start the cutscene and kick off a new autosave.
Blight-queller unlocked as I killed the last darkspawn in the Alienage after about a dozen runs.
When first attempting this method, I chose Allistair, Morrigan, and Wynne as my party. Each Alienage run would crash after about two minutes of play. Some sources have observed this and indicated that too many darkspawn were spawning in the area, causing the game and the Xbox 360 to crash. I did observe the crashing, but may have identified the source: Wynne casting haste as a tactic.
Throughout the game, I had Wynne casting haste as a 'self > any' tactic throughout much of the game and didn't see a crash. It began happening regularly at the Alienage, and I noticed on two occasions Wynne, on screen, in the exact same spellcasting pose as the game froze and the Xbox 360 become unresponsive. I narrowed it down to this tactic. I then reloaded the game at the March to Denerim, chose my party omitting her, and continued as indicated in the guide above.
Edit, 9/5/13: According to PuckJunkie in the comments below, there may have been a patch that removes the requirement that the MAIN character must make the kills. Other members in your party *while under your control* may also count kills toward the total. Secondary confirmation is appreciated, and I can update this solution guide if made - I have not tested it personally.
Edit, 3/6/17 (Six years later!!): Thanks to GrimmLAN13 for confirming that this solution still works in the back compat version on Xbox One!!