Arcana Heart 3

Ok, this information is based on numerous sources, I'll be sure to give credit where is due. Because of the complete mystery this achievement was to me, I started googling around finding the best bits of info.

First of all, what is this RP? This was my first big doubt. Thanks to http://arcana.mizuumi.net/wiki/Game_Modes:

"CHARM stands for Contract of Holy ARcana Maiden. Depending on your records, your compatibility with any of the 23 maidens will change. Every time you finish a match, you will earn Relational Points (RP). The more you deepen your bond, that is, the more RP you earn for any particular character, the softer their expressions will become towards you and the more colors you can unlock."

So, when you complete a match online you'll receive RP points which in turn will let you "level up" your relation with each girl. You'll more RP if you do special conditions, like winning 2 straight rounds, finishing a round with a special, critical heart, etc. You get the idea.

Now, thanks to Setsuna x360a from http://www.xbox360achievements.org/
"To reach an RP level 10 with a character you must accumulate about 200,000 RP points with them online. Refer to "Your Love Expands From The Spirit World " for more information."

The extra info:
"This will be the longest tedious achievement of this game. RP is earned through your performances in online matches. You gain points just for playing in a match however its a very low amount, the real points are earned by doing any of the following in an online match:
Win
No Damage
Straight
K.O
Perfect
Super Finish
Critical Heart Finish
Extend
Arcana
Blaze
First Attack
You need to get every character to at least 10,000 RP points for them to be level 3, if you were to win every ranked match with at least 1,000 points you would need to play at least 230 games however that will probably not be the case. You can boost in player matches however the points you get for winning are greatly reduced and the amount of bonuses you can receive are down to winning and first attacks."

Now, where to see your current RP level with each girl? When you join a ranked match, you'll have about 30 seconds to press Y and enter CHARM which is a ridiculous small ammount of time.
The best way I found out was by creating a player match for 2 players, 1 of the spots private so no one joins. In here, you can also enter CHARM but without any time limit.

(original post of Setsuna x360a: http://www.xbox360achievements.org/forum/showthread.php?t=28...)