The Dungeon Shop is available to players who have unlocked the first Dungeon, Cloudtop Peak. The shop offers various Character Memory Shards and Equipment Pieces. The shop's currency is Dungeon Coins and it can be instantly refreshed for an initial cost of 10 Dungeon Coins.
Dungeon Coins are obtained by winning "checkpoint" battles during a Dungeon attempt (identified by a red chest instead of the usual brown). The amount of Coins rewarded are based on the Dungeon difficulty level. Defeating the Dungeon's boss will also reward an additional Coin reward.
All Dungeon rewards (including Coins) can be doubled by purchasing the Daily Jewel Pack. This microtransaction also provides players with some Premium Jewels and Skip Tickets per day on top of the doubling bonus.
The following characters' Memory Shards are primarilly obtained through the Dungeon Shop. It is highly recommended to only purchase Character Memory Shards from the Dungeon Shop, as equipment is much easier/possible to obtain from simply clearing Main Story Quests rather than using the relatively precious Dungeon Coins.
Dungeon Shop Characters (800 Coins for 5 Memory Shards):
I recommend using your first Dungeon Coins on the following:
Upgrading Yukari. Yukari is a very common 1* Gacha recruitment and an excellent general support for Story and PvP to 2* rarity. This will improve her utility significantly and is obtainable for very few Dungeon Coins.
Recruiting Maho and Nozomi. If a player is unable to pull either Maho or Nozomi from the Gacha, then recruiting them from the Dungeon is an excellent way to guarantee recruiting them into their roster. Maho is an excellent Support and single-target Healer who can carry parties in Story and has good utility in PvP. Nozomi is an excellent Tank who can taunt enemies to protect her allies.