For reaching certain milestones throughout the game, you will get certain medals appended to your Guild Card. Note that some of these will replace older ones as your achievements become greater.

Medal	How to unlock
Azure Rainforest	Reach B11F in the Labyrinth.
Beginning Hunter	Log some of the monsters found in the Labyrinth.
Beginning Surveyor	Complete one floor map of the Labyrinth.
Cache Hoarder	Open up all of the chests in the Labyrinth.
Cache Novice	Open up some of the chests in the Labyrinth.
Cache Seeker	Open up half of the chests in the Labyrinth.
Claret Hollows	Reach B26F in the Labyrinth.
Classic Mode Complete	Complet the game in Classic Mode.
Devoted Scavenger	Log half of the materials found in the Labyrinth.
Dogged Killer	Kill many of the shiny "rare" breeds of monster.
Etria's Guide	Complete half of the floor maps in the Labyrinth.
Etrian Fixer	Complete half of the quests from the pub.
Etrian Gofer	Complete some of the quests from the pub.
Lost Shinjuku	Reach B21F in the Labyrinth.
Lustre Chaser	Kill 100 of the shiny "rare" breeds of monster.
Novice Scavenger	Log some of the materials found in the Labyrinth.
Primitive Jungle	Reach B6F in the Labyrinth.
Quest Complete	Complete all of the quests from the pub.
Rare Breed Killer	Kill one of the shiny "rare" breeds of monster.
Sandy Barrens	Reach B16F in the Labyrinth.
Seven Kings' Grimoires	Complete the ultimate Grimoire Stone.
Story Mode Complete	Finish the game in Story Mode.
Veteran Hunter	Log half of the monsters found in the Labyrinth.
Yggdrasil Core Destroyed	Beat the Yggdrasil Core in the post-game (which is without the Yggdra Virus and Kupala) on Expert.
Yggdrasil's Artisan	Complete all of the floor maps in the Labyrinth.
Yggdrasil's Bounty	Log all of the materials found in the Labyrinth.
Yggdrasil's Hunter	Log all of the monsters found in the Labyrinth.