Easy.
>technically surpassed humanity and became Chaos itself by the time of the DLC, doesn't have to worry about death from the Death Note
>can just keep repeating time loops until he figures it out
>should be able to pinpoint darkness/emotions thanks to how Chaos powers works
>in the event he somehow loses, goes back in time and simply has all the knowledge he gained in a cycle which makes it easier for him to narrow it down