It is helpful to bring along Gau and have him use the Lich or any other undeadRage, immunizing him to Death. The Lich Rage works best because it can use Fira as its secondary attack. As with all undead enemies, the Death Warden can be defeated instantly by using a Phoenix Down on it.
Though the Death Warden has a Rage, it does not appear on the Veldt due to a programming error, so Gau cannot learn the Rage without the use of cheating devices. This error was somewhat fixed in the Advance and mobile versions; the battle in the Cave on the Veldt still uses the wrong enemy formation, but the fight in the new Soul Shrine uses the correct one, allowing him to appear on the Veldt.