I'm not sure how many people know this yet, so I'm going to post it here.
To make the Crux Convergence public event heroic, you have to shoot all of the drones that appear around the Crux; not 100% sure how many times you have to clear all the drones (I assume each phase of the event like with the Glimmer Extraction), but you need to act fast in destroying the drones since they only last I wanna say 10 to 20 seconds. The ones FLYING around the Crux are the hardest to destroy since they're the ones that move the most, while the ones ON the Crux are easier.
I hope this helps anyone trying to complete the Public Hero triumph.