Here is a beginners guide to Legendary:
Follow the link, it has very useful tips and stragies. It is the first video in a series of walkthrough episodes to get you through it. Look in the related videos for the next video.
Read on for tips of my own from my experience of legendary. Before you read on can I just say if you are going to get all the audio files complete the game before doing so. Also, rember you are not master chief, you have stamina and your health doesn't recharge and you take damage from falling from high hights. I would say the campaign is much easier to complete on Legendary than Halo 3s. If you just got ODST then you might as well do it first time on Legendary for all the achievments.
-Use ammo wisely and sparingly. It is best to aim for headshots on every enemy as this kills them quicker. Try to aim for sticks, pick up as much grenades as possible. Do not waste grenades they can be just as important as gun ammo sometimes.
-Work out which enemies are agressive shooters and which are less and base your strategies around this.
-Always take your time. If you die don't give up. Try different tactics to get through.
-Try not to get checkpoints when your bar is red and bleeping. There are plenty of health packs if you just look around. I always heal up just to be on the safe side.
-Try to sneak past enemies: for example, hunters (as they need to be stuck 4 times to be killed and so have a large amount of health and damage). This can be easily done and will make the campaign shorter.
-Do not use the weapons: shotgun and assault rifle. They are useless in this game. Good combinations of weapons include the carbine and plasma pistol, pistol and plasma pistol. The plasma pistol can take off brute's armour/clothes and then they are 1 shot in the head with the carbine or pistol. Pick up jackals snipers as it is just 2 body shots to kill a brute (I think).
-Take out enemies from a distance (especially grunts). Take cover and do not rush, you will get nowhere doing this.
-Let the AI be the distraction. As you go through the game you'll find teamates, you can use them as the distraction as they have infinate health. You can come up from behind the enemy while they are attacking the AI and stick them for example.
Hope my tips and also the walkthrough videos help, thanks and good luck.