So you get this by claiming a certain number of boons off each Olympic God.
(cant remember how many, if someone wants to confirm a number?)
All but one are available after a few runs (no matter how far you get), whilst Demeter requires you to reach the surface (you dont have to beat the final boss though).
When looking at their page, it will state how many more boons are required to unlock the next entry, just keep claiming until it says "Entry Complete".
If you're missing a specific God, then equipping their keepsake at the start of the run will give you one straight away, as well as making them more likely to reappear through the run.
God keepsakes are earned after offering 1 nectar before claiming the boon.
As far as i'm aware theres no 'hearts' level attached, just claiming boons.