"By bonding with many people, Orpheus was once again born from the sea of the soul. He has awakened to the power of Cipher, which holds endless possibilities."
—Persona 3 compendium
Orpheus Telos can only be obtained by maxing out every single Social Link in one playthrough. Once the protagonist has completed all of the prerequisites, Igor will award the protagonist the Cipher's Mask AKA the Colorless Mask in the Velvet Room, allowing him to summon Orpheus Telos from the sea of the soul.
In the events of creating Orpheus Telos, Orpheus Telos of the Fool Arcana truly stands for nothingness, undefined and having limitless possibilities, as Orpheus Telos has only one skill, Victory Cry, a passive skill which completely restores HP and SP at the end of each battle. The rest of Orpheus Telos' skills can only be acquired via the predecessor Personas used to fuse him.
Orpheus Telos is normally created via hexagon fusion, but there are also several triangle fusions that will result in him (most involving either Messiah or Thanatos). In such cases, he will only inherit up to five skills, depending on how many the predecessor Personas know.
Persona Q: Shadow of the Labyrinth
"By bonding with many people, Orpheus was once again born from the sea of the soul. He has awakened to the power of the Cipher, which holds endless possibilities."
—Persona Q compendium
Orpheus Telos is the second free DLC Sub-Persona, released along with Thanatos and Magatsu-Izanagi (who are not free). His unique skill is Healing Harp, which restores the party's HP and removes ailments and Binds for 3 turns.
Medium Phys attack. If unhurt during turn, extra attack activates. (1 enemy)
Slightly restore SP at the end of the turn.
Raise attack/defense and accuracy/evasion for 3 turns. (1 ally)
4 heavy Phys attacks. (1 enemy) Stronger in Boost.
Heavy Fire attack. (1 enemy)
Severe Almighty attack. (All enemies)
3-10 severe Phys attacks to random targets. (All enemies) Stronger in Boost.
Orpheus Telos model from Persona 3 FES
Orpheus Telos from Persona 3 Portable
Orpheus Telos as he appears in Persona Q
Orpheus Kai, the Japanese name, translates to Orpheus Modified, a call back to the Japanese names of the Prime Personas in the Persona 2 duology.
Although the female protagonist's Orpheus has a different design and coloration than the male's does, the female's Orpheus Telos is exactly the same.
The compendium's description of Orpheus Telos (describing his "endless possibilities") matches the ability to completely customize his skills, as Orpheus Telos' skill list depends solely on the skills of the Personas used to fuse him.