In Destiny 2, triggering the Heroic version of the Vex Crossroads public event is relatively simple. Play through the event like normal, killing the Vex until the percentage hits 100. Once the Vex are dead and the Gatekeepers come out, choose a side and take them down. Grab their charges and place them on either side of the gate. This will turn the man-cannon around and launch you over to an island. Destroy the Keeper of Ages here and slam their charge into the middle of the island.
This is where things change. Instead of returning to the central area, look to the back of the island. There will be a crystal floating in the air. Naturally, you'll want to shoot this until it explodes. The destruction of the crystal will create a platform. Jump on the new platform and look for more crystals in the air. Repeat this process until you reach the top of the island.
Once up here, stand on the middle plate to turn the Public Event Heroic. Finish the event, and you will be rewarded with two chests and a heap of XP. You do not need to destroy the crystals on both islands. You only need to destroy one.
Be sure to check out our Destiny 2 Heroic Public Events guide to learn about them all.