Sanity Slippage: At the start of the film, he's enamored with the sun and spends time basking in sunlight. As the movie progresses, his fixation on the sun leads him to spend more time bathing in sunlight, so much so that his face is badly sunburned.
The Shrink: He serves as a mental health professional for the Icarus 2 crew.
Asian and Nerdy: He's of Asian ancestry, and knowledgeable enough about science to navigate the Icarus 2.
Despair Event Horizon: After he unwittingly jeopardizes the mission, Trey succumbs to depression and is put on suicide watch.
Driven to Suicide: His crewmates find him in the medical ward with his wrists cut. While his death appears to be a suicide, Word of God states that Pinbacker did it.
It's All My Fault: When he resets Icarus 2's new course, he forgets to conduct calculations for the shields, which leaves the ship vulnerable to the sun's intense heat and jeopardizes the mission. He's horrified when he realizes his mistake.
Ax-Crazy: The Pinbacker that the Icarus 2 crew encounters is delusional and murderous.
Bald of Evil: Likely burned off, as the man has been exposed to too much sunlight due to his madness.
Big Bad: Sabotaged his mission, sabotaging the second Icarus as well.
Body Horror: Because of his prolonged exposure to sunlight, he's covered in third degree burns. Also, during his fight with Capa and Cassie at the end of the film, Cassie grabs his arm, and his skin and flesh slough off in her hand.
The Fatalist: After his sanity slippage, he concludes that efforts to save humanity are futile.
Pinbacker: All our science, all our hopes, our dreams, are foolish! In the face of this, we are dust, nothing more. Unto this dust, we return. When he chooses for us to die, it is not our place to challenge God.
Implacable Man: He's convinced that God wants humanity to die so that they can ascend to heaven. He meets any attempt to thwart this with violence, and he cannot be reasoned with or cowed.
Made of Iron: There's no reason he's pretty much completely indestructible. He just is. Despite already being covered in third-degree burns.
Nietzsche Wannabe: In his lunacy, he concludes that humanity's efforts to restart the sun are in vain, and that humans are inconsequential "dust" before God.
Not Quite Dead: Pinbacker was believed to have died along with the crew of the Icarus 1. However, he's very much alive and determined to thwart the Icarus 2 mission.
Religious Bruiser: He's a formidable opponent who believes that he's carrying out the will of God.
Sanity Slippage: Pinbacker lost his sanity while leading the crew of the Icarus 1.
Satanic Archetype: He acts as an adversary to humanity on God's behalf (or so he believes in his madness), bringing to mind Satan's traditional role in the Hebrew Bible as the Adversary. When Capa meets him face-to-face, he's bathed in light, evoking Lucifer as an angel of light.
Space Madness: During Icarus 1's journey, he went insane, presumably from the stresses of the mission.
Spanner in the Works: After he goes insane, he sabotages the Icarus 1 mission and creates enormous problems for the Icarus 2 mission.