Princess Arena Shop
The Princess Arena Shop is available to players that have unlocked the Princess Battle Arena (Story Mode Mission 8-15). The shop offers various Character Memory Shards and Equipment Pieces. The currency for the Princess Arena Shop is "Princess Arena Coins," which are distinct from Arena Coins and are obtained from maintaining a certain Rank in the Princess Arena game mode.
Princess Arena Coins
Princess Arena Coins are obtained from maintaining a particular Rank in the Princess Arena game mode. Coin generation is listed as Coins / Hour and range from 0 Coins (e.g. Unranked) to 50 Coins (Highest Ranks). Coins are provided every few minutes based on this rate, meaning a player's actual generation may change as their Rank moves up and down throughout the hour.
Players will also receive 10 Princess Arena Coins upon a successful defense against an opponent in Princess Arena. A maximum of 50 Princess Arena Coins can be earned per day in this manner.
A player needs to maintain a coin generation rate of 34 Coins / Hour in order to purchase one pack of Character Memory Shards (5 Shards) per day.
The following characters' Memory Shards are primarilly obtained through the Princess Arena Shop. It is highly recommended to only purchase Character Memory Shards from the Princess Arena Shop, as equipment is much easier/possible to obtain from simply clearing Main Story Quests rather than using the relatively precious Dungeon Coins.
Princess Arena Shop Characters (800 Coins for 5 Memory Shards):
I recommend using your first Princess Arena Coins on the following:
Recruiting Miyako. If a player is unable to pull Miyako from the Gacha, then recruiting them from the Princess Arena Shop is an excellent way to guarantee recruiting them into their roster. Miyako is an excellent Physical Tank even when compared to other Tank characters. She is a required party member for the Very Hard Dungeon Boss Stall Strategy.
Recruiting Anna and/or Hatsune. If a player is unable to pull either Anna or Hatsune from the Gacha, then recruiting them from the Princess Arena Shop is an excellent way to guarantee recruiting them into their roster. Anna and Hatsune are both excellent PvP Magic DPS characters that are common sights in PvP parties.
(Clan Battle prioritizing, otherwise skip) Recruiting/Ascending Kaori and Suzuna. If a player is unable to pull either Kaori or Suzuna from the Gacha, then recruiting them from the Princess Arena Shop is an excellent way to guarantee recruiting them into their roster. Both Kaori and Suzuna are great characters in Clan Battle, as they can be paired with physical defense shredders such as Makoto or Jun to significantly increase their damage output. However, if a player does not care about Clan Battle, they should not spend the Princess Arena Coins to recruit Kaori or Suzuna, as the 15 days worth of Coins at baseline generation rates can be better spent on recruiting other characters with more utility.