Overview
Medals are "achievements" that you earn after doing certain milestones. You can view the medals you've earned and those that others have earned when you look at a character profile.
List
Thanks to sdjx22 who complied this list on the English forum - see the thread here.
Adventurer Set (Not specific to the adventurer character class)
1) Adventurer (Bronze) - Complete 10 quests.
2) Veteran Adventurer (Silver) - Complete 40 quests.
3) Story Line Lover (Gold) - Complete 90 quests.
Sleeping Set
1) Sleepyhead (Silver) - Sleep twice in a row.
2) Sleepwalker (Gold) - Sleep three times in a row.
Fort Fighter Set
1) Fort Fighter (Bronze) - Take part in one fort battle.
2) Veteran Fort Fighter (Silver) - Take part in 25 fort battles.
3) Fort Battle Guru (Gold)- Take part in fort battles (unknown number).
Fort Battle Winner Set
1) Fort Battle Winner (Bronze) - Take part in one fort battle, and be on the winning side.
2) Veteran Fort Battle Winner (Silver) - Take part in fort battles, and be on the winning side (unknown number).
Praying Set
1) Believer (Bronze) - Pray 10 times.
2) Monastery Resident (Silver) - Pray 250 times (unconfirmed).
3) Bishop (Gold) - Pray (unknown number of times, possibly 500).
Construction Set
1) Construction Worker (Bronze) - Build 200 construction points.
2) Architect (Silver) - Build 3000 construction points.
Building Set
1) Builder (Bronze) - Finish the construction of a town building (not the last level of a building).
2) Master Builder (Silver) - Finishing the upgrade of 5 different levels of the same building (unconfirmed).
3) Puh, the Last Nail (Gold)
Sacrifices Set
1) No Victories Without Sacrifice (Bronze) - Lose duels against an NPC (Non Playing Character, i.e. a quest duel) 50 times.
2) I'm Used to This (Silver) - Lose duels against an NPC 250 times.
3) Master of the Underworld (Gold) -Lose duels against an NPC 500 times.
Combative Set (On beta, unconfirmed on a 'real' world)
1) Combative (Bronze) - Believed to be for dueling and not being hit (unconfirmed).
Tourist Set (On beta, unconfirmed on 'real' worlds)
1) Tourist (Bronze)
2) Backpacker (Silver)
3) Globetrotter (Gold)
Rowdy Set (On beta, unconfirmed on 'real' worlds)
1) Rowdy (Bronze)
2) Ruffian (Silver) - For wining 100 duels (NPC wins not counted).
Chicken Set
1) Chicken (Silver) - Rumour has it this set is to do with calling a fort battle but not taking part in it.
Wreath Medals
Trainee Builder - For levelling up (experience wise) with the experience earnt from construction.
Construction Fool - For building with 0% motivation (On Beta and German worlds).
The Flag - Find the product Union Flag from the job Guarding the Fort (On beta, unconfirmed on 'real' worlds).
Development Aid Volunteer - For spending or transferring nuggets (On beta, unconfirmed on 'real' worlds).