The difficulty definitely picks up since the Library (I'm playing this on Easy, BTW).
Well, there's your problem! Play through on at least Heroic. You may want to hook up a second controller and play through Legendary on co-op so you have infinite lives. Get used to playing the game on more challenging modes. I've solo'd all the games in the series on Legendary (except 2 because it sucks) and they are insanely fun. The assault rifle is completely useless on Legendary, so you are forced to use more interesting weapons and to make every round count. The 2-weapon limit makes the game like a puzzle: you have to know what's ahead and carry the best two weapons for the job if you hope to survive. The Elite AI in Halo 1 is second to none on Legendary; outsmarting and out-shooting an elite in a one-on-one encounter will make a man outta you.