I was already thinking about fishing when I read your title, but it seems you hate it
(how can anyone hate fishing
), so never mind about that..
Here are some which are (somewhat) effective ways of gaining achievements in a reasonable time:
1. Run TBC and WotLK instances in heroic mode, those usually give you two achievements per run, and also boost your reputation to certain factions, which means even more achievements when you hit exalted
2. As said above, farming factions to exalted by various ways of doing dailies, ordinary quests and running instances (all of those three count towards other achievements as well)
3. World events give a nice amount of points as well (although very stupid to recommend doing world event achievements, when there aren't any in August)
4. Explorer, seriously, do Explorer. Put on some music/a TV-show/movie of your choice, grab a snack and hop on that Wind Rider! It doesn't take very long if done correctly, and just tedious at most