From Destinypedia, the Destiny wiki
Tier I Guide
Players must kill as much Taken as they can before time runs out. Defeating Taken in rapid succession grants more progress, but if the players don't kill the Taken fast enough the progress will go down. Eventually when players reach 100% they will have to fight and kill a boss.
Tier II Guide
After completing the first objective of killing taken, a black gate opposite of the cliff will open presenting a bridge that the player will have to construct, to construct the bridge, the player will initially have a 50 second timer to capture the first section of the bridge and 30 seconds on the rest. The enemies on the bridge will consist of mainly 3 types, hordes of taken thrall will attach from behind and the front, accompanied with a major enemy that spawns each time the player captures a section of the bridge, and from both sides on top of floating pyramids snipers. Upon capturing the final section of the bridge a portal will appear, taking the player into an obscure area surrounded by pillars with 2 named boss Knight that have a large amount of resistance and health, the player will need to kill both of them before the timer reachs 0, to make that possible he will need to kill a major enemy that ramdomly spawn on one of the 4 corners of the map, by doing so a well of light will appear, granting a great damage buff to all players that are within.
Tier III Guide
Tier 3 is similar to Tier II, however, enemies have higher hp and damage, bridges take 20 seconds to capture (try to keep at least 3 players on at all times to ensure completion), and Oryx summons a lot more adds.
An emblem can be obtained if you do each Tier III boss without a death (individual basis). There is also a Triumph for completing the bridge without anyone on the team using a super.
List of appearances