lol
I just started legendary today. I have never done a legendary run in any Halo game (highest I'd go is heroic).
In the first level, I kept dying in two spots: the part where there are skirmishers to the left and right, with grunts in the center and elites at the end, and at the end of the first level, when you're in space.
And oh god. Those grunts and their fuel rod cannons.
Best advice i can give you for a solo legendary play through is to always have a precision weapon on hand. DMR, BR, Light rifle, Carbine, pistol, or boltshot. Take out the grunts and jackles first before even worrying about elites. Only worry about them if they should rush you down, but that rarely happens
After taking out the grunts and jackles you can easily mop up the elites with Plasma Pistol > Head shot.
Same thing goes for fighting promethians. Kill all the crawlers and watchers before taking on the knights. Plasma pistol still works well against knights, but you have to be more precise to get the headshot.
Last thing i can say is take your time. If you are running low on ammo then don't be afraid to backtrack to fill up.
If you run into any other problem areas let me know and i can help you out.