If anyone knows if you can get achievements in co-op or on custom maps, if you know feel free to comment.
Also, for whatever reason Prodeus achievements are all hidden by default, to see their descriptions either check global stats or the in game achievements menu.

-Getting By
"Finish 10 Levels"

-It's Finally Over
"Finish The Campaign"

-Kill 100 Enemies
"Kill 100 Enemies"

-Kill 1000 Enemies
"Kill 1000 Enemies"

-Kill 10000 Enemies
"Kill 10000 Enemies"

These are all self-explanatory.
-Multi-Kill 5
"Kill 5 Enemies In A Row"

-Multi-Kill 10
"Kill 10 Enemies In A Row"

The descriptions are misleading, instead of killing 5 or 10 enemies in a row you have to kill them with a single shot. Use explosives, like rockets or grenades
-Splatter Master
"Obliterate 100 Enemies"

I have no idea what this means but you'll definitely get this just by playing. (UPDATE: apparently it means attacking an enemy until it's corpse explodes)
-Fist Parade
"Obliterate An Enemy With Your Fists"

I got this by killing the first enemy in the game with my fists.
-Shield Breaker
"Break 10 Shields"

Near the end of the game enemies will have big red shields around them. Break 10 of them to get this achievement.

-Friendly-Fire 20
"Get 20 Enemies To Kill Each Other With Friendly Fire"

You'll probably get this just by playing the game, if not try to get enemies to run into fire from other enemies.
-Cloak And Dagger
"Kill 10 Cloaked Enemies"

A while after the half way point in the campaign, cloaked enemies start to appear. They're mostly invisible but you can still see them, kinda like spectres from DOOM. Kill 10 of them to get this achievement.
-Watch Your Step
"Kill 20 Enemies With Environmental Hazards"

Simply kill 20 enemies with explosive barrels.
-In-Fight 100
"Get 100 Enemies To Kill Each Other"

You probably noticed that normal and blue enemies tend to fight, simply let 100 of them kill each other.
-Corrosive
"Melt 20 Enemies With The Chaos Caster"

Near the end of the game, in the level "Frost", you get the Chaos Caster. Kill 20 enemies with it to get this achievement.

-Mopping Up
"Kill All Enemies In A Level"

-Explorer
"Find All Secrets In A Level"

-No Big Deal
"Finish A Level Without Dying"

-Kind Of A Big Deal
"Finish A Level Without Dying On Hard Difficulty"

-Completionist
"Finish A Level with 100% On Any Difficulty"

-A Really Big Deal
"Finish A Level with 100% On Hardest Difficulty"

Complete a level with every enemy killed, every secret obtained and without dying on Ultra Hard and you'll get all of these.
-Pacifist
"Finish A Level Without Killing Any Enemies"

-Hard Target
"Finish A Level Without Taking Damage"

These are both pretty hard, one because avoiding damage is hard and one because not all levels can be completed pacifist. For some reason completing challenge levels doesn't count. If you have both the dash and double jump, you can do both of these on the first level. I recorded a video showing how.

-Go Get Some Fresh Air
"Finish The Campaign With 100% On All Levels"
This one will take the longest to get.
Zero Master upload a 100% speedrun, you can use that as a guide since he shows all of the secrets (and ores)

pagb666 is also making dedicated level guides, here's his video for level 1, the playlist link is in the description.

-Pocket Money
"Pick Up 10 Ore"

-I'm Rich
"Pick Up 25 Ore"

-Imagine the Wealth
"Pick Up 50 Ore"

You'll find ore laying around levels.
-Little Spender
"Make 1 Purchase"

-Big Spender
"Make 5 Purchases"

Go to the level "Shop", and spend ore in exchange for weapons and abilities.
-Hidden Exit
"Find A Hidden Exit In A Level"

The only hidden exit that I know of is in the level "Meltdown". You need both the dash and double jump. Here's a video:

Thanks for reading my guide! If you have any feedback let me know.