Normally, if you're using the same GFWL account, it doesn't matter where you got the game from. You'll already have the achievements and will not be able to earn them a second time. Achievements are tied to your GFWL account, not the CD key you use to install the game.
Arkham Asylum is a bit of an exception, however. There are two separate versions of this game on GFWL: The original and the Game Of The Year edition. The achievement list for each version is exactly the same, but GFWL considers them two different games and you can earn the achievements for both. (I'm not sure why Microsoft/Warner Bros/Rocksteady did things this way, but it's definitely an exception and not the rule. The GOTY edition of Arkham City will not be a separate game.)
The Batman Franchise Pack on Steam includes the GOTY edition of Arkham Asylum. If the version you played before was also the GOTY edition, then you've already earned the achievements for that version of the game and won't be able to get them a second time. Otherwise, enjoy your additional 1000 Gamerscore.