This achievement is a long haul, It's taken me a long while to get all 3...and to be honest it can get pretty repetitive/boring as you progress.
All you gotta do is get experience, however there are many ways to do this. In particular I did the whole game solo on hard for every mission. Although tricky, I was able to get bonus amounts of exp, whilst also honing my skills.
You have access to two 'Subclasses' the second of which you'll unlock at lvl 15 (though after doing this for your first character, the other two will be obtainable from the start!). Wait to do this one as you'll already have a lot of progress done for the basic subclass.
ALWAYS have bounties active. I do all story/co-op player ones available for the boost of exp, and it's very high.
Daily challenges are helpful as are weekly ones. You may need a friend or two to help you out.
Strikes are good for exp, but you might wanna get a friend or two to help speed things along. Me and a friend of mine did about 10+ strike playlists on the lvl 24 setting. We also got a lot of currency/nice loot.
You can also trade in stacks of 50x materials (i.e. Spinmetal, Helium, Spirit Blossom or Relic Shards) for a boost of exp, but it will take you a while to amass the needed amount.
The cryptarch at the tower will be your port of call a lot, and as you bring him engrams he'll start levelling your cryptarch lvl. Doing this is easy (I'm as of writing half way through lvl 5) and nets you a big amount of exp.
Hope this helps guys!
Also; for those having trouble unlocking glitchy achievement do this:
Press the Menu button RB over to settings, highlight Log Out and choose Switch Profile (not Change Character). This will take you back to the game start screen, and once you press A, it will ask you to choose your Xbox Live profile.
Choose your profile and then choose your character from the character select screen. Any achievements that should have been unlocked will then unlock.
*Cheers to FLEEBS & ludo10109 for the info