Completing reputation achievements can be time consuming, but the odds are good that you've already completed some of them retroactively. Practically all reputation achievements can be completed by increasing your reputation with various factions, so if you're already exalted with some factions, you will automatically unlock the associated achievements. Completing unfinished reputation achievements can reveal cool aspects about the world that you might have missed the previous time you played through, so it's definitely worth spending the time.
Ambassador of the Alliance/Ambassador of the Horde
If you're exalted with all five of your home factions, you will earn the special title of Ambassador before your name. Your status will count toward the achievements for becoming exalted with a large number of factions, and any race-specific mounts you get will count toward the mount achievements. You can also go into the Alterac Valley battleground and do the turn-in item quests to increase your reputation. Turn in blocks of Storm Crystals to gain additional reputation.
The best tip for quickly increasing your reputation is to do all of the low-level quests, even level-1 quests, for a particular race. These quests are easy to complete, and they will increase your reputation. In addition, it can be fun to see some quests you haven't seen before.
Northrend Vanguard
You can earn this achievement by reaching an exalted reputation with the Argent Crusade, the Wyrmrest Accord, the Kirin Tor, and the Knights of the Ebon Blade. Northrend's daily quests can get you to exalted with many of Northrend's factions. Just make sure you do those daily quests, well, daily.
Some Northrend factions, including the four mentioned above, give you a tabard when you're friendly with them. This tabard allows you to gain reputation with them when you're in any Northrend Heroic dungeon. Make sure you have your tabard on when you visit those dungeons!
