A qilin that has obtained a king is likewise a creature without a lifespan, but this one disease has no cure.
Literal
King [object-を] obtained qilin [also-も][additionally-また] lifespan [object-を] not-have creature [copula-だ][but-が], this disease [in particular-ばかりは] cure [of-の] method [subject-が] not-exist.
Almost certainly from the Japanese fantasy series 十二国記 (Juuni Kokuki / The Twelve Kingdoms), where 麒麟 (qilin, mythical Chinese creatures) are spiritually bonded to their chosen kings and share in their near-immortality. 王を得た is a past-tense relative clause modifying 麒麟 ('a qilin that has obtained a king'). ばかりは is a contrastive combination meaning 'this one (in particular), contrary to the general case,' often emphasizing a single exception to an otherwise-stated rule.