Copied from the walkthrough for convenience to anyone in future:
Kingdom Two Crowns WalkthroughThis achievement can be done co-op only! So save up 20 coins with one player and let the other one leave all their coins and gems behind the wall. Run towards the Greed and let them take your shiny crown. Walk back inside and let the other player purchase a new crown for 20 coins. If you do this by the eighth day, you will unlock the achievement above.
Think this may of changed in an update, it was only 8 coins for me