Just finished Halo 4 on solo Legendary and like those above I've a few tips which others may find useful.
Running is your best friend in the earlier levels. On later levels I found that the more I tried to skip a mob, I'd either just get mauled to death or in one instance I managed to sequence break the game (leading to me having to restart the level from roughly the half way point) so you do need to be careful later on. This tactic did save my bacon on several occasions in levels 2-5 though so don't feel obliged to kill everything.
Unlike Bungie's Halo games, when you die in a vehicle the game does NOT save the vehicle damage you've taken to that point. Essentially meaning you can take a massive beating, hit a checkpoint, get yourself killed and then have a completely restored vehicle upon respawning. This works with all vehicles in the game including the Mantis. Traditionally, I've always found Halo's vehicle sections to be the most challenging and this turned those levels into a walk in the park for me.
Lastly, instead of using Hologram on the last level, I found it more achievable using Auto Sentry. Not only does the Auto Sentry draw fire as Hologram does but it also aids you in conserving Light Rifle ammo (fuck I'd HATE to have to do the last 3 islands with just a Boltshot), the only drawback is that the recharge time on Auto Sentry is fairly long so you'll have to employ plenty of patience, which you should have anyway if you are playing the game on solo legendary.
That's all I can think of for now, but I'll add more if anything does spring to mind.