Keep in mind two things with this guide:
1) It won't fully take you by the hand and it means you play a bit the game while using it to understand certain mechanics. It's a quick strategy guide to help you getting all the achievements without redoing a second playthrough because some are heavily missable.

2) This guide is obsviously full of spoilers. 50% of the APPEAL of the game is about DISCOVERING new units, secrets and such by yourself. If you'r the guy (or the girl) who prefer to avoid spoil, I recommend using this guide for a second playthrough. Why the second you may ask? Because it will keep all your progress through the tech tree (yes, like your New Game +) and may be faster than the first due to powerfull ressources and units.

What is Devouring Stars?
It's a short RTS game where you get the control of very few units. If you have played Grey Goo, units are really similar to the slow Goo mothers, gathering ressources and able to fight and reproduce different units. The difference here is all the units have the ability to gather stars and fight, and are obtained by fusing. Also the number of stars gathered is directly related to the firepower of their owners. Interesting game with great OST, albeit being maybe a bit repetitive and short (4 hours or so to complete the campain). Multiplayer included though.

Enemy portal
Escape through an enemy portal


You first achievement. Escaping through an enemy portal is mandatory to win a level.

Crossfire
Win against two armies


Some missions involve more than one army. Missing them is VERY UNLIKELY that's why I put it in this category.

General
Fight a strong entity


Again, you will eventually be led in a mission again a greater unit, so almost unmissable.

Chaos!
Rebuild Chaos


At some point into the game, you will be able to build Chaos, the most powerfull unit. Chaos is also linked to the story: another mandatory achievement.

Armada
Start a run with 8 entities


Each time you clear a path you are awarded by a bonus slot to make your army stronger. Before reaching the end of the game, you will be able to unlock more than 5 slots, meaning you will also be able to create an army of more than 8 units.

Finish the game
Finish the first game cycle


Self-explanatory: finish the campain.

Parasite
Take control of more than 5 units with Clotho


Clotho is available in the Control Path of the "tech tree". After building him, you can possess an enemy unit during a short time by right clicking on him. Keep in mind you need enough stars, if not, nothing will happen. Do that 5 times. This is not mandatory to do it in one level.

Freeze
Freeze more than 10 enemies with Aether


Same thing than Clotho's related achievement. Aether can paralyse more than one unit at a time, just try to get as many stars as possible. This is not mandatory to do it in one level.

Destroyer
Destroy more than 4 entities with Phaeton


This one might be hard because I believe you have to destroy 4 entities at a time. Build Phaeton (Control Path) and lead him to a position he will be surrounded by 4 or more enemy units and hope the explosion kill all of them.

Sniper
Use Orion more than 5 times


Orion is the most powerful unit of the Combat path (Chaos for the Gathering Path and Rhea for the Control Path respectively). By right clicking in a enemy unit with Orion, you bombard it with your stars. You will need to gather many stars with Orion as stars will be depleted for each bombardment, so help it with your gathering units like Demeter or Chaos and transfer stars to Orion (double-clinking on Orion while they are close to it).

Learned
Access the full reference trees


Simply try to discover every combinations. Get access to your "tech trees" or "paths" by clicking on the icon above or using tab.

Alone
Start a level with more than 5 enemies against one of yours


You can't do it by simply beginning a mission as you will have more than 1 unit at a time. You have then 2 strategies for completing your mission with one unit (and then getting the achievement at the start of the second mission). Either you try to build an unique and powerful unit like Chaos and reach the portal or else try to quickly reach the portal with a unit like Janus and sacrifice all of your remaining units.

Perfection
Finish 10 runs in a row without dying


This one sounds hard at first sight, but is rather easy once you collected powerful units for your next missions or once you get Chaos.

You will probably use this guide for those achievements alone: they can happen randomly and are difficult to find. You even may overlook them so be careful and follow this section.

All the stars
Gather all the stars with Curbas


This secret can only be found in the early game. If you are far advanced into the game (like I was), you may have to finish the first cycle and try to get it in the New Game +.
After clearing your first or second path, you may find an odd audio and visual noise while rotating the map like this:



As soon as you see that happening, stop rotating the map to discover and alternate path like this one:



Do you see the black symbol? This is the last mission of this path and leads to a secret place:



In this level, at one moment, the narrator will ask you to make a dance for him. Just do it by clicking repeatedly to the right and to the left of your entity. Completing this mission will give you a consumable and powerful ability "Curbas" which can make one of your unit absorbing all the stars in one level (stars will be lost after reaching the portal though).

Hephaistos
Discover Hephaistos hideout and survive


During midgame you will discover a cyan-colored and friendly tribe: the Ardieis. Find one mission where you can find an isolated Ardiei trying to build a portal to escape:



The secret place is located in this portal, so you have to help him to build it. There are two ways to do it. Either you try to protect him during his process (long and hard), else you may control him with the help of Clotho (fast, but still need protection from your units). Just getting Clotho ingame is enough to control all of the Ardieis (get in mind for the maps where you can find many Ardieis units, they are really powerful!).

The secret level:



To escape this level, you have to collect enough stars to reach the Hephaistos' forge exit. First, make a Clotho unit and bring all of the Ardieis to your Clotho. Then gather all Ardieis' stars by double-clicking repeatedly on Clotho until you stole almost all the stars:



Break in the rhombus and create a copy of the symbol in its center by splitting Clotho and making another entity (here Briareos). Doing this, you will gather bonus stars:



"Consume" the rhombus:



With enough stars you will be enough powerful to beat the 4 guardians:



This secret also gives you powerful Golem units.

Furies
Put off the furies


During midgame you may also randomly come upon a strange guardian:



This most likely will happen in "Balanced" or "Unbalanced" levels but it is recommended to always be prepared to face such a scenario. As its secret is really hard, you have to be prepared to be able to create your most powerfull unit: Chaos. It is indeed only possible to follow the strange guardian in the secret level with ONE UNIT. If you do it with more (like I did the first time) only one unit will be selected to reach the secret level.



So build the godlike Chaos fast and follow the guardian. He's really fast, but don't worry, you will eventually get to the secret level:



Gather as many stars as possible, because the fight will be intense: the enemies will arrive in after less than a minute and are invisible. Try to beat them one by one. Good luck. Achieving this mission will give you bonus units: the furries.

All the bonus powerful units and abilities you can unlock: