I’m not sure that video choice is helping you here. In the video Link is showing no emotion through either his movement or facial expressions, which makes the VA’s job monumentally harder. Try a more expressive cutscene from a recent game perhaps? The voice must sound natural and not like it’s being read from a script (difficult). Lastly, enunciate! Every crack in your voice, change of pitch or mispronunciation will be picked up by a good mic.
I would first break up large dialogues into shorter ones and join them up paying particular attention to continuity. Then when your voice adjusts to this kind of stress, take a stab at the lengthier dialogues.