Library was not hard on legendary, just irritating and boring and far too long to play through by yourself.
T&R on legendary is damn hard when going solo. I am yet to beat it without a co-op partner and it is the same damn room everytime. I usually am able to manage until there are 3 invisible elites lurking around and then I am completely screwed.
Two Betrayals was hard if only for the Banshee part. You have 2 options - snipe the Covie elites and hope the Flood survive long enough for you to do a good job, or try and bumrush past everything.
Keyes was irritating as well. Though I found the outside portion a little harder. There are plenty of places to hide and backtracking + shooting makes things a little easier when it comes to the flood. Also, like most levels, if you have a co-op partner you can beat each other through some of the doors and skip entire sections.