Shiki Ryougi's Mystic Eyes of Death Perception (Kara no Kyoukai) grant her the ability to kill off just about anything (distance, special abilities, ghosts, etc...) as she can see their lines of existence. Immortality won't mean much if Shiki is able to literally kill such a concept.
Garlic Jr has what the OBD calls type four immortality: he is granted immortality from a source, and to defeat that, you would need something of a higher source to destroy that immortality.
The only suggestion that I see here that would definitely KILL him (not just BFR or something) is the Giga Slave. Obviously, Lord of Nightmares>>>>>>>>>>>>>>>>>>>>>>Shenron.
Saint Seiya has a lot of shit that could probably do it, but if it's just a brute force attack (ex: Athena Exclamation), it probably won't work though it would knock him flat on his ass. Ki would not do it nor I think would soul manipulation on its own as Garlic's immortality would counteract it.
Sailor Cosmos has basically the powers of the souls of the entire galaxy and was able to take out the personification of all evil (albeit only temporarily) in that galaxy so maybe she can do it, but I don't know. Dark Schneider's Judas Pain is a higher source of power than the Dragon Balls but still I'm not sure if his moves would kill him on their own because as stated before, firepower alone won't work. Shiki Ryougi sounds promising.
My understanding of true immortality is that your physical and spiritual body cannot be permanently killed. All damage will be mystically healed.
@Nevermind: what you say makes sense, a higher being would have to remove the immortality. e.g. Porunga > Shenron. So Porunga would be able to undo the wish, with his power returning Garlic.Jr to his Mortal Status.
But then again this is not KILLING an immortal, because Garlic is no longer immortal :P I guess its a bit of an oxymoron or something. lol If it were possible to kill an immortal, then they are obviously not immortal. LMAO!
@MisterShin: He was a true immortal though the only way to kill him was to destroy the Wailing Wall which was one of Hades source of life, you also had to destroy Elysium, and The Underworld in order to kill him which were Athena's intentions. If she would've just killed Hades he would've simply come back another few centuries. He has the power to bring anyone back from the dead except for Gods .