During the Vex Construction event you need to stop Vex from reaching a central core that they wish to integrate with. It is basically a horde mode where you have to kill everything that spawns, before it can reach its goal. To activate the Vex Construction Heroic Event you still need to do this, but you also need to destroy three plates that can be found in the area.
To find the plates, look at the central core. It will have three lines of energy traveling outwards from it. Follow the lines and at the end of them will be a plate. You need to control the plate until the counter reaches one hundred, then the plate will be destroyed. You need to do this for each of the three plates, all the time stopping the Vex from reaching the center. This is definitely an event that is easier with a Fireteam as you do have a time restriction. Whilst you are on the plates Vex Fanatics will spawn. Be sure to kill these exploding enemies from a safe distance.
After you have destroyed all three of the plates, you will need to survive against a flood of Vex enemies. They will still be intent on making it to the core. There will be multiple Hydras that spawn during this portion of the Vex Construction Heroic event, so take them out quickly. There will also be two Cyclops enemies that spawn in, these can do massive amounts of damage so be sure to take them out also.
Once the timer runs all the way down, you have completed the Vex Construction Heroic event and it is time to collect your loot from the chest that will spawn in.
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