The following page lists all of the reactions necessary:
http://doodlegod.wikia.com/wiki/Philosopher's_stone
Update: September 18, 2015
This is now obtainable. You need to be on version 3.0.1.25 for this to unlock. Check your version before trying. If you already completed this you should be able to update and then complete another match with the Philosopher Stone and this should unlock.
At the time of this update I can't seem to get this new version to download so I haven't unlocked this. Hopefully this gets pushed to all users soon.
You can also reference this guide at Gamefaqs.
http://www.gamefaqs.com/iphone/998670-doodle-god/faqs/68098IEdit 12 august 2018
If you're having issues try this:
Go back to Episode 2 and combine Quicksilver with a Demigod