I've beat crota as the sword holder many times on Normal but i have finally done it on hard mode as a Titan!
enjoy the gameplay guys
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40+ HM Crota kills with the my Titan holding the sword. http://destinytracker.com/destiny/videos/xbox/ThamaJama/1d3a094b-53a0-4375-9374-ba5d7e43c74b http://destinytracker.com/destiny/videos/xbox/ThamaJama/2cef8ac8-7884-4e38-8b16-a8b377c21a80 Couple of clips. Enjoy.