。
I tried to read the writing on the wall.
Literal
Wall [on-に] written characters [object-を] decipher tried.
判読する means 'to decipher/make out' — stronger than just 読む, implying the text is hard to read. ~しようとした is 'tried to do' — volitional + とする in the past. 壁に書かれた is a passive relative clause: 'characters that were written on the wall.'