This guide serves as a wrapper for other guides. I'll link most of the guides in the guide section here to make it easier to look.

Obtained by following tutorials.

Push and Turn
Unlock a Treasure Chest


The first Treasure Chest should be easy to find. There is also a Treasure Chest in Aurora Village so all you have to do is to get a key (which is easily obtained in the first few areas). In order to unlock the Treasure Chest, press the arrow which is shown in the right side of the key before the time runs out.

Well on your Way
Pick Up an Ability Orb


You'll find it in the first few areas.

Distant Thunder
Use the DUST STORM on Fidget's Projectiles


Press K, L (while still holding K) to activate Dust Storm with Projectiles.

With Great Power...
Level Up by Assigning Skill Gems


You have to level up to unlock this tutorial.

Obtained through story progression and can't be missed.

Defused
Defeat Fuse


Defeat the first boss.

Waters of Life
Defeat Lady Tethys


Defeat the second boss.

High Spirits
Defeat Baron Kane


Defeat the third boss.

...And the Dust Settles
Defeat General Gaius


Defeat the final boss.

Bringer of Death
Kill 500 Enemies


It shouldn't be hard to get this. I get it in Chapter 1.

Sad Way to Go
Kill an enemy with the slide attack


You'll unlock sliding attack in Chapter 2. Do it on any of the weaker enemies to make it easier.

Blue Bomber
Simultaneously Kill 6 Enemies with a Single Bomb


Follow this guide.
If you follow the guide, you can get the achievement when you go to Forgotten Meadow.

A Decent Start...
Successfully complete a 200+ hit combo


That's More Like It
Successfully complete a 1000+ hit combo


There are a lot of guides for this. I personally use this guide.
If you follow the guide, you can get the achievement when you go to Forgotten Meadow.
Note that there is also a sidequest for this at the end of Chapter 1.

The Blacksmith of Archers' Pass
Meet Haley


Go to the Blacksmith in Archers' Pass. Obtainable after you finish the first objective of "The Blacksmith" sidequest.

Paragon
Opt out of putting poison ivy into Gianni's laundry


Renegade
Reign chaos by putting poison ivy into Gianni's laundry


In "Out to Dry" sidequest, you are tasked to go to Ivydale Glen to save a kid. After you killed two giants, head down below and save in a separate slot (or just make sure you didn't hit another save point before you finish the quest). You'll find a basket on the west and you'll be given two options. The option that you choose will determine the achievement that you'll get. Report the quest and load the game after you get an achievement and choose the other option to get both of them in one go.

Opposite of Fail
Complete all Fale Quests


Fale is in Aurora Village. There are 6 quests in total which consists of ingredients gathering. You can buy the ingredients in the shop (after registering the items). Obtainable in Chapter 1 after Abadis Forest is unlocked.
This[elysiantail.wikia.com] material list can help you if you don't want to buy the materials to complete the sidequests.

One Last Wish
Fulfill Bopo’s wish for snow


Complete "Snowflake" sidequest. Available at the end of Chapter 2 and clearable after Blackmoor Mountains is unlocked in Chapter 3. In order to finish the sidequest, go to the circled area in the picture below in Blackmoor Mountains and drop down in the unstable platform near a tent in the background and head west to get a Cooler.
After that, go to the save point to the east for a cutscene. Report to Bopo in Mudpot.

Friend of Falana
Complete 5 Sidequests


Hero of Falana
Complete 10 Sidequests


Savior of Falana
Complete 20 Sidequests


There are 21 sidequests in total. There is a sidequest list here.
The guide list all but one sidequest: A New Venture, which is obtainable by talking to any merchant outside Aurora Village.

An Impressive Display
Earn a Four-Star Rating in any Challenge Arena


The Stuff of Legends
Earn a Four-Star Rating in EVERY Challenge Arena


Follow this guide.
It's recommended to do the first two trials later on since it involves in killing enemies.
For Cirelian Trial #4, you can either pass through the zombies or do the trial later on to kill them easily.

Wait, aren't you...?
Unlock a Cage and Rescue a Friend


Baker's Dozen
Hang out with Twelve Friends in the Sanctuary


There is a cage list here.

Note that you need to get all upgrades and resonance stones in order to save all Friends. Here are the upgrade lists:
- Chapter 2: sliding
- Chapter 3: gripping vine
- Chapter 4: double jump
- Chapter 5: jump boost (in wind current)

After you rescue all Friends, go to Sanctuary to get the achievement.

Bad Therapist
Bug Matti


Talk to Matti in Archers' Pass 5 times.

Tinkerer
Craft an item from a blueprint


Self explanatory.

Cutting It Close
Successfully Parry with less than 10% health remaining


It's easier to do this from a save point in case you messed up.

Silence Those Guns
Destroy every enemy Cannon


In Everdawn Basin, destroy all 4 Cannons.

Above and Beyond the Call
Complete the Game on Tough or Hardcore setting


Tough is easier than Hardcore.
In Tough difficulty, you can recover a maximum of one bar of health in a save point.

Finding All of the Cages
How to get the Side Missions Achievements!
Yet another 1k Combo guide (Video)
A Simple Guide - How to make a 6 bomb-kills
4-Star Challenge Arena Guide
Materials[elysiantail.wikia.com]