Here is a short and quick guide on how to get all of the different achievements for Geneforge 1 - Mutagen.

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These are the achievements that you are more than likely to get while just playing through the game, and don't really require you to do anything specific.
These achievements can get obtained on any difficulty, all of the achievements requiring difficulty levels will be listed down below in another section at the bottom.

Have To Learn Fast - Just complete the first few tutorial areas and this achievement will pop.

The Obedient - Reach the city of Pentil. You don't really need to do anything special to get inside.

The Vengeful - Reach the city of Kazg. You can enter from the North, which requires finding a spy in the top left corner of the map, which requires some Leadership. Or you can enter from the South, but it will require you to fight some crazed Serviles.

No More Pencils - Head to the ruined Shaper School area, and meet the Servant Mind there.

The Secret - Learn about what Sucia island has hidden away, the Geneforge! It is impossible to not get this achievement by just playing through the game.

Source of The Infection - All you need to do is enter the Research Halls area of the map. You will need to do this to get to the Geneforge and finish the game one way or another.

The Traitor - Head to the very North Western part of the map. It will be pretty difficult to get there at lower levels, but at higher levels you will be fine. Talk to the Shaper Goettsch there, and you will get this achievement. No need to kill him or work for him, just meet him.

Novice Explorer - Clear ten zones on the map and turn them green by defeating all of the enemies, destroying all the enemy spawners, making peace with the people who live there, or just getting to the other side(s) alive, etc.

Experienced Explorer - Same as above, but for 40 zones instead of 10. This is barely half of the map, so you will get this just by playing the game.

It is a good idea to play through a section of the game and meet all of the different Servile leaders. Save your game before you make any commitments to the different Servile groups, and you can actually get all of these achievements in one go by reloading saves, before reloading to your preferred group.

Turn Traitor - Join up with the Takers faction, who you will most likely meet last. They will ask you to kill a bunch of Sholai interlopers hiding in some caves to the East. This will deprive you of some allies later on in the game.

Your Service Is Welcomed - Join up with the Obeyers faction. You will most likely meet them second. They will ask you to feed nutrient goo to a Servant Mind in the Spiral Burrow. Not hard, but it does use up one of the limited amounts of Mind Food that can be found in the game.

Tend Towards Justice - Join up with the Awakened faction, who you will meet first and very early on. You will be asked to do a pretty easy task to get into their good graces.

A New King Rises - Join up with Tajkov and let him use the Geneforge. No matter what you do throughout the game up to that point you will always have this option open to you. He will ask you to get him some Shaper Gloves. These can be found in the top left of The Great Temple, home to Goettsch. You don't need to kill Goettsch to get the gloves, but you will need to have a decent Mechanics level.

These are some of the achievements that you can get near the end of the game that have to do with the Geneforge, and are optional.

Finishing What Others Started - Destroy the Geneforge. Requires you to have found a control rod in order to safely destroy the crystal power sources, but you can do it by brute force. Control rods can be found in the South Workshop, Trajkov's personal chambers, the Northern Mines, and more.

Taking The Opportunity - Use the Geneforge on yourself. You will need to get the Shaper Gloves from Goettsch, look up at the previous section and the A New King Rises achievement for more information.

You can actually get these two achievements one after the other; using the Geneforge and then destroying it. It is recommended you make a save before picking one of these, as you cannot reverse the choice.

Here are some achievements that don't really fit anywhere, and that can be missed while playing the game.

Idle Enjoyment - Pop fifty of the orbs that spawn while on the main menu by clicking on them, super easy, if a bit boring. Thanks to some helpful comments, you may be able to skip the boredom by clicking on the orbs multiple times very quickly.

Claim The Mines - This entire area of the map can be avoided, so you may not get this one. You will need to feed and wake up the Servant Mind in the Mine Core, ask him to disable the traps in one of the adjacent areas, and go to that area.

Came To Get Rich - Have 5000 gold in your inventory. This one is pretty easy to get if you are playing on a lighter difficulty, or are just frugal and prefer going back to cities rather than using items. Make sure that you empty out the gold from the merchants of the Servile factions you intend to destroy, as merchant gold capacity is limited.

Royal Sampler - This one requires you to have some Shaping skills. You will need a level three creation in your party of each type of shaping, as well as a Cockatrice. So a Cockatrice, a Drayk, a Battle Alpha, and a Glaahk (or their varients). To get the Cockatrice help out Servant Mind Swanick in Barrens Research, or Ascended Sessina in the Ascended Labs.

Promising Research - Once you have either helped the Sholai in the caves, or killed them for the Takers, you will be able to go to the Eastern Docks. There you will find Shaper Thrakerzod. He wants you to deliver a sample of red goo from Yu-La, who can be found in Barrens Research.

History Lesson - In order to get this one and learn the ancient secret of the island, you need to travel to the Spirit's City section of the map and talk to the shade inside the temple. To do that you will need to touch the specially marked pylons in the following maps in the following order: Drayk's Vale, Ancient Crypt, Diarazad, The Junkyard, Dry Wastes, Western Wastes, Valley of Ghosts, and finally the Spirit City. After touching the last pylon, you will be able to enter the main room and talk to the shade.

You can actually brute force the History Lesson achievement by spamming Essence Shield and healing spells, entering the temple and quickly talking to the ghost, going where he asks, and then talking to him again.

The Inner Crypt - To get this one you need to pass through the Shaper Crypt and enter the Inner Crypt. You will need to be a decently high level to get this, and collect the two orbs that will unlock the door. The two orbs can be obtained by killing specially marked Thahds in the Western Wastes map and the Drayk's Vale map. They may not always spawn, so it is likely you will need to go back a few times to check for them.

Linguist Under Pressure - Master the Sholai language by finding 4 pieces total of a mix of learning materials, or lessons in person, on the language. These can be found in various areas, such as the Refugee Cave, Wooded Valley, archives in Kazg, The Crossroads, from Learned Jaffe of the Obeyers, etc. Just explore around (and don't kill all of the Sholai) and you should get it easily.

Traps 101 - Reach the Servant Mind in the Hill of Jars. You can just pass over this area in the early game and come back later with better mechanics, a ton of living tools, or items like the Tinkers Gloves and Dante's Guile.

Return to Terrestia - Complete the game while still getting a good ending. As far as I can tell, this just means don't side with the Takers, or Goettsch. Using canisters, using the Geneforge, siding with Trajkov, leaving the Geneforge intact, even killing the innocent Shapers in the Eastern Docks doesn't seem to give you a bad ending.

Warning: Just to note, you cannot lower the difficulty level at any point of the game if you want to obtain these achievements. So if you want ones that can only be unlocked on Veteran difficulty, you need to play through the game on that difficulty from the very start.

A Sad Tale Ends - Defeat Oroborus on Veteran or higher. This one is actually pretty difficult at that level, but if you have played through most of the game, or have used the Geneforge, you should be able to manage this one. She can be found in the Barrens Bunker, unlocked by Ascended Alonzo, after you have helped Ascended Sessina defeat a Cockatrice.

I think you can try and lead her into the room next door, and activate the incinerator there to destroy her, but I never attempted this.

Bold Escape - Beat the game and get a good ending while playing on Veteran or higher.

Amazing Escape - Beat the game and get a good ending while playing on Torment. Good luck.

The above two achievements there say you require a good ending, more information on that can be found at the top with Return To Terrestia.

Path of The Pacifist - Beat the game on Normal difficulty or higher without ever attacking. This also counts your shaped creations and their attacks.

I Walk Alone - Never make a shaped creation and beat the game on Normal difficulty or higher.

These last two can actually be done at the same time, and it is probably recommended you do it that way too. No need for creations if you are going a Pacifist route.

Thanks for reading this guide! I hope it helped you out somewhat. A big thanks to Mechalibur and the Spiderweb Software forums for helping me out with some of these. If anyone has any questions after reading all this I will try my best to answer.