You will find Engrams throughout you journey in Destiny, they look at a glance the same as weapon/armour drops. Once you find an Engram you must go to the Tower and talk to the merchant on the right as you land to see about getting it Decrypted.
Considering this is a drop-based achievement this could take you a few hours to a few days. However if you buy engrams from the merchant I cannot confirm if they count towards this achievement. That said I would say from my experience it
seemed to help.
*EDIT 1: You CAN buy engrams from the merchant for progress on this achievement. Thanks to Vermigs for confirmation *
If you're desperate for the achievement all I can advise is to go to a low level area (Earth, where the broken ship is to the north of where you land in Patrol is a good spot) and farm enemy kills. If you're a much higher level they'll fall like rain and you may get a few Engrams.
Hope this helps!
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