Defeat Hades with at least one heat activated to reveal this prophecy. The actual prophecy is to defeat each of the enemies listed that gets benefits from the "Benefits Package". The Benefits Package is one of the heat conditions that can be activated at the Pact of Punishment before starting a run. It gives 2 heat. Turning this on and doing multiple runs is about all the advice I can give on this one. The enemies will spawn randomly.
Here is a list of the enemies and what they do that I found from user Jerry9_ on reddit:
Shifter (green ghost)
The enemy will teleport randomly.
The enemy has greatly increased health and size.
The enemy deals more damage, like the Hard Labor punishment. Not sure of the percentage or if it stacks with the punishment.
Puller (purple disk)
The enemy has a small 'gravitational' field around them that can not be escaped by walking. Usually takes several dashes to break free.
Savior (blue shield)
The enemy will periodically give other nearly enemies 1 shielded health, up to a max of 5.
The enemy attacks and moves faster, like the Forced Overtime punishment. Not sure of the percentage or if it stacks with the punishment.
Linker (pink ray)
A laser is created from the enemy to another nearby enemy. Prioritizes linking with armored foes, but can link to normal enemies.
Tartarus only. Fake clones of the enemy will constantly spawn, up to a cap. Each clone has 2 hp (1 armor, 1 regular). All clones die when the original dies.
Asphodel only. The enemy will constantly create fire traps.
Seeker (green star)
Projectiles fired by this enemy will home in on you.
Popper (warrior soul)
Warrior enemies in Elysium only. Upon death, the foe will drop many fake souls that explode upon death or after a few seconds.