After doing a Game Sync, you can find and meet conditions for medals, as below, on the Global Link.

Medal	How to unlock
Ace Pilot	Use Fly in the field many times.
Archeology Lover	Revive a Pokemon from a fossil.
Battle Learner	Fight 100 battles.
Battle Maison 20-Win Streak (Double)	Compelte 20 Double Battles in a row at the Battle Maison.
Battle Maison 20-Win Streak (Multi)	Compelte 20 Multi Battles in a row at the Battle Maison.
Battle Maison 20-Win Streak (Rotation)	Compelte 20 Rotration Battles in a row at the Battle Maison.
Battle Maison 20-Win Streak (Single)	Complete 20 Single Battles in a row at the Battle Maison.
Battle Maison 20-Win Streak (Triple)	Compelte 20 Triple Battles in a row at the Battle Maison.
Battle Teacher	Fight 200 battles.
Battle Veteran	Fight 400 battles.
Beginning Trader	Use Link Trade once.
Berry Gardener	Pick 10 Berries from fields.
Berry Scientist	Create a mutated Berry.
Broad Friendship	Register 30 Friend Codes.
Busy Save	Save 20 times.
Central Kalos Pokedex Completionist	Complete the Central Kalos Pokedex.
Coastal Kalos Pokedex Completionist	Complete the Coastal Kalos Pokedex.
Duke	Become a Duke at the Battle Chateau.
Earl	Become an Earl at the Battle Chateau.
Easy Cycling	Ride a Bicycle 30 times.
Egg Beginner	Hatch a Pokemon Egg.
Evolution Hopeful	Evolve one Pokemon.
Evolution Tech	Evolve 10 Pokemon.
Exp. Millionaire	Earn 1,000,000 EXP. in 24 hours.
Experienced Saver	Save 50 times.
Extensive Friendship	Register 10 Friend Codes.
First Encounter	Meet a real-life player in the game.
First Friend	Register one Friend Code.
Fledgling Photographer	Send one photo to the Pokemon Global Link (PGL).
Frequent Trader	Use Link Trade fifty times.
Friend Safari 10	Have 10 encounters in the Pokemon Safari.
Good Rod Fisherman	Find 10 Pokemon when fishing.
Great Customer	Spend $100,000 at PokeMarts.
Happy Birthday	Get a birthday wish through the PSS.
Hard Cycling	Ride a Bicycle 100 times.
Heavy Walker	Walk 20,000 steps.
Honored Footprints	Walk 100,000 steps.
Light Walker	Walk 5,000 steps.
Link Battle Amateur	Fight one Link Battle.
Lumiose Explorer	Explore much of Lumiose City and become very stylish.
Lumiose Tourist	Explore some of Lumiose City and become a little stylish.
Marquis	Become a Marquis at the Battle Chateau.
Middle Walker	Walk 10,000 steps.
Moderate Customer	Spend $10,000 at PokeMarts.
Mountain Kalos Pokedex Completionist	Complete the Mountain Kalos Pokedex.
Noneffective Artist	Mistakenly use moves that are not effective (i.e. Electric on Ground).
O-Power Lv. 1	Use an O-Power once.
O-Power Lv. 2	Use an O-Power ten times.
O-Power Lv. 3	Use an O-Power 50 times.
Occasional Trader	Use Link Trade ten times.
Old Rod Fisherman	Find a Pokemon when fishing once.
Outgoing	Meet 10,000 real-life players in the game.
Pedaling Legend	Ride a Bicycle 500 times.
Pokemon Center Fan	Rest your Pokemon at a Center many times.
Pokemon-Amie Aficionado	Play with a Pokemon in Pokemon-Amie 10 times.
PR Video Debut	Make one PR Video and show it off.
Regular Customer	Keep going to PokeMarts, becoming regular customers.
Smart Shopper	Get a Premier Ball (buy 10+ Poke Balls).
Sociable	Meet 100 real-life players in the game.
Starter Cycling	Ride a Bicycle once.
Step-by-Step Saver	Save 10 times.
Successor in the Making	Get a Pokemon to Mega Evolve.
Super-Training Instructor	Play with a Pokemon in Super Training 10 times.
Supereffective Savant	Repeatedly abuse type weaknesses (i.e. Fire on Grass).
Sweet Home	Return to your hometown (Vaniville Town).
Trash Master	Check empty trash cans.
Trick Master	Use many tricks on Roller Skates.
Viscount	Become a Viscount at the Battle Chateau.
Wonder Writer	Save 100 times.