Although Pokémon-Amie can Increase the Friendship, it and Affection are Separate Values and having Five Hearts is not considered Maximized Friendship, as Levelling up with Five Hearts does not necessarily evolve Pokémon that require High Friendship.
Azurill evolves into Marill when Levelled up with High Happiness. In Pokémon X and Y you can Increase a Pokémon's Happiness by:
Walking 128 steps
Getting a Massage (Cyllage City)
Soothing Bag from Super Training
Using EV Reducing Berries
Soothe Bell (Shalour City)
You can also Reduces a Pokémon's Happiness by:
Using Bitter Medicine
So try to not let your Azurill Faint in Battle and don't give it any Bitter Medicine such as Revival Herbs.
Note: Trading will Reset your Base Friendship
After your Azurill has evolved into a Marill, your Marill should evolve into Azumarill as soon as it reaches it's next Level or straight away if a Rare Candy is used on it since Marill is supposed to evolve at Level 18 and yours is Level 27.