Rushabhdev (Adinath) achieved moksha by following the traditional path of a Tirthankar:

• Renunciation: After ruling as king, he gave up worldly life and distributed his kingdom to his heirs.
• Spiritual effort: He spent a long period doing intense tapas and meditation to conquer inner passions.
• Kevala jnana: Through his austerities, he attained kevala jnana (omniscience), the clear, all-knowing vision that makes one a Jina.
• Moksha: With kevala jnana and the right conduct, he departed from the cycle of birth and death and attained nirvana, traditionally said to be on Mount Ashtapada (often identified with Mount Kailash).

Note on traditions:

• Both Digambar and Shwetambar traditions describe the same sequence—renunciation, kevala jnana, and moksha. The primary point of variation is sometimes the exact place or details of the events, but the essence remains the same: Rushabhdev ends the cycle of rebirth at Ashtapada.

You can read more about his life and path of moksha here and about his life details here