Defeat three of the Girsh nephilim in a single playthrough.
Kill three of the six Girsh Nephilim in a single playthrough, abilities of previous killed Girsh Nephilim will be added to the rest of them.
He
Defeat five of the Girsh nephilim in a single playthrough.
Kill five of the six Girsh Nephilim in a single playthrough, abilities of previous killed Girsh Nephilim will be added to the rest of them.
Heat Death
Get vaporized.
To be vaporized your temperature needs to be above 10,000. This can be accomplished with relative ease via being covered in plasma and then detonating multiple thermal grenade mk IIIs on top of your character in quick succession.
This requires the player character to peacefully wake up which can be done by leveling up as the dream character.
The Laws of Physics Are Mere Suggestions, Vol. 3
Prove the information paradox by causing your surroundings to glitch.
Pour a dram of warmstatic onto a nearby item causing it to glitch into a random item.
Total Makeover
Pour a dram of pure warm static on yourself.
Pouring warm static on yourself is potentially irreversible including when using Precognition as the mutation can be removed. However as a truekin, you can always reverse the result via use of a sphynxsalt injector.
Vav
Defeat six of the Girsh nephilim in a single playthrough.
Kill all of the Girsh Nephilim in a single playthrough, abilities of previous killed Girsh Nephilim will be added to the rest of them.
Beguiling a creature with an innate ranged attack such as a slugsnout and then standing directly between it and an enemy should be a reliable way to accomplish this.
spiral borers.
dreamcrungle whilst already within a waking dream.
temple mecha mk Ia, a 
temple mecha mk II or a 
temple mecha mk Ib, can be done by force interacting with it and then selecting the Infiltrate option, an infiltration will have a 10% chance to succeed.
thermal grenade mk IIIs on top of your character in quick succession.
Thicksalt during a water ritual for -50 reputation.
Slog of the Cloaca during a water ritual for -50 reputation.
sunslag can be rarely found in a 
swollen bulb by plucking coral from a 
palladium strut with coral growth. It can also be purchased from 
ichor merchants and the 
alchemist
warm static onto a nearby item causing it to glitch into a random item.
Precognition as the mutation can be removed. However as a truekin, you can always reverse the result via use of a 
sphynx salt injector.
amaranthine prism.
hookahs can be commonly found around the stiltgrounds and require at least one dram of fresh water to be smoked from.
adiyy, who are located within the Banana groves near the spindle.
Aoyg-No-Longer, servant of Ptoh in the Cosmic Wood is found at the bottom of Eyn Roj.
Beguiling a creature with an innate ranged attack such as a 
slugsnout and then standing directly between it and an enemy should be a reliable way to accomplish this.
Corpus Choliys to cure it.
crumpled sheet of paper to 
Eskhind or to 
Warden Neelahind.