This achievement is a bit of a grind, so strap in.
The easiest way I found to level up is to speedrun the main mission quests because they give a high amount of experience. Generally, I avoided fighting enemies whenever possible, just to speed the process up (individuals give relatively little experience).
The Trickster Rogue is probably the best character for doing this quickly, as proven by the fact that in dungeons I (and other TRs if they were there) would have insanely high damage in the scoreboards at the end (e.g. me at 4mil against the next best at 1.5mil).
The main thing to beware when doing this is that there is a chance that you will be slightly under levelled going to the next area, however the areas are not as difficult as you may expect.
If you get to a level high enough to move to the next area even if you haven't finished the current one then just skip ahead because the missions there will give more exp. Then, if you need some extra exp from somewhere just go back to the ones you skipped.
Invoke after every couple of hours for bonus exp.
Azure enchantments give experience boost in utility slot (4% at rank 3).
Sometimes Arc will hold a double exp weekend event (such as on 24/4/15) which speeds this up massively, I got my second character to level 60 in a day doing this method on double exp.
Once you have your first character to level 60 you can refine azure enchantments with your high wealth for the maximum experience boost. You can also purchase a second horse, a companion (or use your upgraded companion) and lots of health potions/injury kits. You can also have other enchantments to speed up your second playthrough (off and def slots). Once you have these items, go to a mailbox in Protector's Enclave and compose a mail including your items and send it to @[Your Gamertag]. This will send the items to all of your characters (not duplicated, all characters can open this message and receive the items).
Go to your second character, take the items and equip the companion. Then play through by the same method for the first character. Once you hit level 60 the achievement will pop.
As pointed out by InconSteveable; "two important zones to complete are the Blacklake District and Neverdeath Graveyard. The final quests in these areas provide bags as rewards."