Destiny 2: Forsaken is a large expansion to the base game, offering a great campaign, tons of new gear to collect, and two new destinations to explore—the Tangled Shore and the Dreaming City.
Both new locations have new public events to take part in in the open world, and triggering the Heroic version of them will offer you even better rewards. Here's how to trigger Heroic in Forsaken's new public events.
Neutralize the Cryo-Pod defenders
A massive cryo-pod holding a prisoner from the Prison of Elders will crash down in the Tangled Shore. A few waves of enemies will spawn, so kill them, and be ready for more.
The cryo-pod will open and a boss will hop out. Deal damage to them in increments, and at some point, the cryo-pod will malfunction and start a damaging Arc field around it. When that happens, look at the cryo-pod itself—two of the vents on its side will be steaming. Shoot them, and an Arc orb will spawn out of it. Pick up the Arc orb and throw it at the boss to stun it.
You must throw three Arc orbs at the boss to freeze it, and trigger Heroic. At that point you must defend the boss while more waves of enemies spawn and the prisoner is prepared for transmat back into prison.
Stop the Ether ritual
The Scorn will be attempting to corrupt Ether, and it's your job to stop them. In this event, there will be multiple Servitors surrounding a Scorn Servitor in the middle. Enemies will spawn to attack you, but the important thing to pay attention to is when Ether will begin to float out of the surrounding Servitors and into the middle.
You must kill each of the three Dredge Chieftain enemies that spawn while preventing any of the Ether from making its way to the Servitor in the center of the ritual. Pay attention to a distinct sound that will let you know when the Ether is spawning, and shoot it out of the air to make it disappear.
Once you do so, Heroic mode will trigger and a reanimated version of one of the Barons will appear. Kill the Baron and win.
The Rift Generator
You will need to defend a generator of a Taken rift while massive waves of Scorn approach you from multiple angles. The closer the enemies get to the core, the lower its integrity gets.
Abomination enemies will spawn, and killing them will drop an Arc charge to repair the core. Just keep fighting enemies and prevent them from making it to the rift generator.
During the onslaught of enemy attacks, Taken Blight bubbles will spawn. Destroy them as fast as you can. Once you do, Heroic will trigger and you will be teleported into the Ascendant Realm where you will have five minutes to take down a boss. Kill it and collect your rewards.