Trueforms are monstrous creatures with dark souls inside of them and they reside in the Asylum . They're one of the strongest enemies in the game. Trueforms are dangerous both up close and from a distance. Also, Trueforms difficult to destroy because they are very agile and have high defense. They are equipped with homing in rockets on their wrists that fire a stream of Dark Soul energy at Shadow Man. Each projectile hit causes 300 damage. Due to their size, Trueforms run around quickly and are hard targets to aim at. They also scratch or stomp on Shadow Man (causing 1500 damage) if he gets too close. Shooting them with the Shadow Gun charged up and using the ensigne (shield) is one way to defeat them. You can also use the Violator if you have it in combination with the Shadow Gun to quickly lower its health.
Legion wanted Jack the Ripper's help to construct the Asylum and include all the “unique and misunderstood individuals” to make an “army of the damned”. The army being the Trueforms to cross the veil to Liveside and bring about an apocalypse that Mama Nettie warns you about in the intro cutscene. The first Trueform seen in the game is in the Asylum Playrooms after Shadow Man let it out of its cage prison, but he won't be able to fight it until later in the game (when he obtains the Marcher Gads.) Also, dead Trueforms can be seen in the Asylum: operation rooms that are filled with the surgeons. The Trueforms are near a machine with a Dark Soul to be put inside of them to reanimate it.
The five serial killers each contain one Dark Soul inside them also which makes them insane much like the Trueforms, they even look like them briefly as they are being shot. They assume the Trueform look once you've lowered their health all the way down before dealing the final blow with the Shadow Gun which is the only way to kill them.