To get the prophecy added to the Fated List of Minor Prophecies you'll need to keep giving Ares nectar gifts on your runs. I think it takes 5 or 6 gifts.
To complete the prophecy you need to have killed 10,000 enemies across all of your runs. Kills attained prior to unlocking the prophecy still count towards this.
You can check how many kills you've attained by using the pool in your room (provided you've built it via the House Contractor).
With the required amount of kills, find Ares on a new run to finish the prophecy. You'll already have Ares' Blood-Filled Vial keepsake, so equip that and you'll be guaranteed to find him.