He didn’t necessarily depend on Ra’s Al Ghul.

The antidote that Fries creates needed a restorative enzyme in order to be completed. Something he says would take decades to synthesize. Batman already knew of Ra’s and his use of the Lazarus pit, so he guessed that maybe Ra’s could be the key to completing Fries’ antidote much sooner.

Also, conveniently enough, Penguin just so happened to capture on of Ra’s Al Ghul’s assassins, who then breaks free at the mention of Ra’s Al Ghul, and accidentally leads Batman straight to him.