Rare medals are used to level up a cards Skilllevel or buying any kinds of Arcana.
Rare medals are also known as "Medals". (for obvious reasons)
Getting Rare Medals
You can get rare medals by trading in your R and above-Cards in the "Edit Unit" section of the Menu for various amounts of medals, ranging from the lowest possible, [25] (Android) and upwards.
Exchanging R and above Cards for Rare Medals
The Medal Girl gives up to [1500] medals which makes her a great source of rare medals without sacrificing too many valuable cards.
She can be obtained by doing Amalgamation with Gold Girl and Metal Slime.
A quick but non-efficient way to obtain a small amount of medals is also Amalgamating a Mechanic and an Enchanter into an Android and exchanging it for [25] which is only a quarter of an usual, unevolved R-Card.
Thus, making the R and above-Card exchange and do some specific quests are the only way and option to recieve any rare medals.