Possible Ideas for Significant Auto Events to Track in Risk of Rain 2:

Grabbing an item (or if that is too much, grabbing a red or yellow rarity item)

Finishing a Boss Fight

Using a Teleporter

Using a Portal

Activating/Finishing a Void Vent

Finishing a Round on Simulacrum

Obliterating

Activating Equipment (Debatable, because of the equipment lunar item)

Hitting Low/Critical Health

Death