Spoiler: Known and speculated how to Activate Heroic Public events

If sources are wanted I'll grab the ones stated elsewhere.

1. Spider Tanks (thank you u/platotudes for that find) require detonating Arc charges to take out shields protecting Scorch Cannons, and using those will activate the Heroic mode which drops another Spider Tank (Walker).

2.Ether extraction seems to be destroying generators during each of the extractions. These seem to be away from the main drill and if all are destroyed will activate the Heroic, which drops in a large sum of glimmer which must then be defended.

3.Ether Resupply which features a giant Servitor. The Servitor has the ability to teleport players in a fashion similar to Orbiks Prime, and can be shielded by lesser Servitors. The Heroic mode seemed to activate while destroying a different servitor which seemed to be giving ether to the larger main boss Servitor, which causes it to go haywire. This causes it to take less damage and it's teleport when used against players causes them to drop from high up, requiring a jump to minimize fall damage.

4.Cabal Excavation seems to be destroying a Thresher (edit: name). Doing so will summon an Extraction Valus who has a standard Minigun.

EDIT: Though I didn't see the Heroic activate, I should mention that Taken Blights are now an actual public event. Speculating on how to activate it's heroic, there was a large blight and a small blight and you chase around the blight. My guess is we destroy the small blight each time it appears to trigger the Heroic version.

Edit 2: u/KeybladeOP Brought up the Injection Rig, which seems to to be a large area under a shield that burns, and destroying the Rig's vents triggers it's heroic. And an event I didn't see unfold, but saw the HUD display, is a Fallen Weapon's Exchange.