The Japanese phrase you found translate into "I'll discern with eyes unclouded, and then decide", as Toritoribe-san said. If that is what you want to say, you are good to go. If you really want it to say "unclouded by hate" then the phrase you found doesn't quite hit the mark.
Even if your quote is used in the English version of Princess Mononoke, it's not completely the same as the original Japanese version. I already gave you the English translation of the original Japanese 曇りなき眼で見定め、決める, and it's different from your English phrase, as Majestic-san already pointed out about the difference. The correct translation of "See with eyes unclouded by hate" should be something like 憎しみの曇りなき眼で見よ since it's an imperative sentence.