Achievements will be presented in the order I unlocked them. Some are unlocked by progressing the story and some are missable and depend on side quests.

The Fallen Hero

Wake up......

Story achievement. You will get this as soon as the game starts.

Nocturnal hunter

You went hunting in the forest at night!

You can miss this one. After eating at Leon's hut, Leon will go outside after telling you to use his bed to rest. Instead of sleeping, follow him. He will tell you about a rare monster hiding in the forest at night. Follow the path to the west, after leaving the hut area. You will find a path that moves in a spiral, follow it and you will come across a monster. Make sure you have a few potions with you. After you beat it and pick up the loot, you get the achievement.

Welcome to North Willow!

Let's get out of this rain!

Story achievement. You will unlock this one when you arrive at North Willow.

A spot of fishing

You relaxed and did a spot of fishing in North Willow

You can miss this one. There are at least two fishing spots around North Willow. They look like the achievement icon so they are easy to spot and they are all available after you spend the night at the town. One is located in the little lake close to the fountain. Another is located outside North Willow (close to where you left your boat the previous night). I used the one at the lake and the achievement unlocked, but I assume you can use any to do it.

The Doughnut Thief!

You solved the case of The Doughnut Thief!

You can miss this one, as it's a side quest. After finishing with the barracks meeting (WARNING : You should do this after the barracks meeting, which is after recruiting Grom and not later on in the game as it will not let you pick up the quest) , head to the bakery and talk to Kev (it's the building next to the fountain). He will ask you if you are looking for work. Say "Yes" and he will ask you to find the thief who keeps stealing his doughnuts. Go outside and you'll find some crumbs on the fountain. Talk to the blonde girl to the left of the fountain, then to the woman to her left. Go to the tavern and you'll find more crumbs. Return to the bakery to see the conclusion and unlock this achievement.

Gear Upgrade!

Grenn Upgraded some of your gear at The Black Anvil!

You can miss this one. Go to Grenn (he is located in the first building you come across when you enter North Willow) and ask him to upgrade your equipment. The option isn't available at first but it becomes available later after Brom joins your party.

Warning : If this is not the first time you are playing the game, remember that you probably need to start a new game to get these new achievements, as mentioned in the patch notes. Using an older save seems to cause crashes whenever you try to start a battle.

You musht Diesh!

I've got a feeling we haven't seen the last of that guy.....

I assume since you need to pass through that place, this is a story achievement and it cannot be missed. In the ruins area, after spending the night at Leon's hut and going for the boat in the morning, you will find the Scaava shown in the achievement icon somewhere in the ruins (the one that wears armor and a cape). Defeat him to receive this achievement.

Fratus The Fantastic!

Look at that stunning painting, Fratus Gabriele is the most famous artist in all of Terra!

This can be missed. Go into the house in the lake in the middle of North Willow. Talk to the man in the house and you will get the achievement.

Toil and Trouble

You recruited Frann!

Story achievement. After recruiting Tybalt, head over to the house at the southwest of town and talk to the girl inside to recruit her!

Nice guy Tybalt...

He's not so bad......for a Bandit!

You can miss this achievement. Talk to the kid near the entrance to the mayor's house. He is somewhere between the fountain and the tree.

Tybalt the Barrel Boy

This is thirty work, let's grab a beer!

This can be missed. After recruiting at least Tybalt (Frann is not required according to carlonimus), talk to the Willow guard inside the barracks (the one located at the left of the table). He will ask you to move a barrel that is right outside the barracks to the Tavern. Go outside, pick up the barrel to the right of the entrance and take it to the Willow Tavern.

Ding dong the witch is dead...

Crazy old hag! What has she gone and done!?

You can miss this one, since it's a side quest. After you pick up Frann, head to the house between the Barracks and the mayor's house entrance. You will find the housing officer there. After he leaves, pick up the key in the house and head over to your own house to unlock the hatch on the floor. Navigate through the underground passages until you find the witch. Kill her and you will get the achievement.

Thank you, Back To Basics Gaming for the correction on this one!

A couple more achievements seem to have been added yesterday and they are related to gold owned.

Saving up for something?

Gather 5000 gold!

Thank you, Sparkly Sparkly Pokon for the verification!

They call me Mr Moneybags!

Gather 15000 gold!

Thank you, MkayShock Madness for the info!

Another seems to have been added today (June 23, 2015)

Do you seek power?

During your stay in the underground passage, follow the doors marked with the blood stains/runes until you reach a huge dragon bone head. Fight and beat the dragon in battle to get the achievement!

Thank you, M@nkey for the info!

Thank you for reading this guide. If you find any errors or come across any additional information I could add, feel free to comment!

Changelog
May 26, 2015 : Updated with new achievements. You musht Diesh!, Fratus The Fantastic!, Toil and Trouble, Nice guy Tybalt..., Ding dong the witch is dead..., Tybalt the Barrel Boy.
May 31, 2015 : Updated Ding dong the witch is dead...It's a side quest and not a story achievement according to the developers.
June 2, 2015 : Updated with the new achievements that were added. Saving up for something? and They call me Mr Moneybags! (Credit goes to MkayShock Madness for this one!).
June 4, 2015 : Updated Saving up for something? with confirmation that it's 5000 gold (Verified by Sparkly Sparkly Pokon).
June 23, 2015 : Updated with the new achievement Do you seek power? that was added today. (Credit goes to M@nkey for letting me know there is a new achievement and the location!)
August 1, 2015 : Corrected a mistake in "Toil and Trouble". Should have been southwest instead of northwest. Thank you, carlonimus!
August 5, 2015 : Verified that Frann is not required for "Tybalt the Barrel Boy". Credit to carlonimus!
August 10, 2015 : Added a warning at "The Doughnut Thief!" since it's possible to lock yourself out of being able to receive the quest. Thanks to carlonimus!