| Arcanis Ultra |
These are the methods I found to achieve varying methods of Immortality, based solely on Class or Race based abilities, barring any magic items or artifacts.
Alchemist - Level 20 - Grand Discovery: Eternal Youth (Revert to youth, Cease aging)
Antipaladin - Level 20 - Archetype: Knight of the Sepulchre; Undying Champion (Become undead)
Druid - Level 5 - Archetype: Reincarnated Druid (Reincarnate if dead)
Monk - Level 20 - Archetype: Monk of the Four Winds; Immortality (Cease aging, reincarnate if killed)
Oracle - Level 20 - Heavens Mystery; Final Revelation (Reincarnate if dead)
Oracle - Level 20 - Occult Mystery; Final Revelation (Become ghost)
Oracle - Level 20 - Solar Mystery; Final Revelation (Cease aging)
Oracle - Level 20 - Time Mystery; Final Revelation (Cease aging)
Oracle - Level 20 - Archetype: Shigenjo; Final Revelation (Reincarnate if dead)
Shaman - Level 20 - Heavens Spirit; Manifestation (Reincarnate if dead)
Sorcerer - Level 20 - Imperious Bloodline (Human Only); Immortal Legend (Cease aging)
Wizard - Level 20 - Arcane Discovery: Immortality (Cease aging)
Living Monolith [Presige] - Level 10 - Ageless Stone (Cease aging)
Agent of the Grave [Prestige] - Level 10 - Undeath Initiate (Become undead through another means, keep faculties)
Mythic - Tier 1 - Universal Path Ability: Longevity (Cease aging)
Gnome [Race] - Survive the Bleaching
Reincarnate [Spell] - Return to life, even if died of old age
Mind Swap [Spell] - Switch bodies with another creature
[The following two ways do not grant true immortality, but can be ways to severely extend one's lifespan]
Sorcerer - Level 20 - Astral Bloodline; Timeless Soul (Become immune to retroactive aging effects when leaving timeless planes)
Arcane Spellcaster - Level 8 Spells - Clone; Temporal Stasis (Create frozen clones to transfer into after aging to near death)
I hope this has helped.