Step 1: Renal safety of a volatile agent depends on how much it is broken down to fluoride. The greater the fluoride load, the higher the risk to the kidney.
Step 2: Rank the agents by metabolism. Desflurane is almost inert, isoflurane is minimally metabolised, and halothane is metabolised to a modest degree but causes hepatic rather than fluoride-related renal injury. Methoxyflurane sits at the extreme end, being very extensively metabolised.
Step 3: Its breakdown, including metabolism within the kidney itself, liberates inorganic fluoride that injures the renal tubules. The result is a characteristic high-output renal failure, and the drug is also associated with hepatotoxicity.
Step 4: For this reason methoxyflurane is the agent to avoid in renal failure, while the other three remain acceptable from a renal standpoint.
\[\boxed{\text{Methoxyflurane}}\]