While wandering throughout the worlds of Destiny you will come across different chests. Some of them can be looted instantly and usually reward you with Glimmer and Hadium Flakes, but some of them require keys to be opened.
Key for Akka Chest is a random reward for completing Wormfeeder Rune task, that asks you to kill 50 hive enemies without dying. This quest chain starts with Wormsinger Rune. Check out our guide How to use and collect Wormsinger rune. The key also randomly drops from enemies in Patrol mode.
Where to find Akka Chest location
The Chest of Akka is to the right facing the Court of Oryx on a platform, crawl through some holes in the wall then check the large room before the room with the Ascendant Soul rock and the Taken Consumption sludge.