Re: ''Three times the amount of medical bills.''
One of the great misunderstandings of this field is that people are somehow entitled to 3 times the amount of their medical bills. What your claim is worth is dependent upon your economic losses (cost of medical care, past and future, lost earnings or ability to earn, past and future, and other out of pocket expenses that are reasonably related to the injury) and non-economic damages, pain, suffering, and emotional distress. Non-economic damages are extremely subjective, but obviously, the more serious and long lasting the injury, the greater the non-economic damages. I have gotten 6 figure awards with $5,000 in medical bills and have gotten $5,000 awards with $4500 in medical bills.
If the defendant's liability is not clear cut, you should be prepared to take less. If you have (and this is one of the insurance companies favorite ploys) "overtreated", they will not offer you much more than your medical bills.
Your letter should include copies of all of the relevant medical records and bills, W-2s or pay stubs verifying your lost earnings claims, and if liability is in issue, all relevant evidence you have on that point. Just be sure you don't give them something you wish you hadn't. But also beware that they will investigate your claim and you probably won't be able to hide anything material. Don't even try to.
Your first paragraph should detail all of the enclosed exhibits and the total amount of your out of pocket economic damages. Next paragraph should contain a discussion of liability. Finally you should explain in detail all of the injuries suffered and the hardships they have caused (i.e. due to shoulder impingement syndrome, I have constant pain in the right shoulder. I cannot lift my arm above shoulder level, etc.) Again be careful here. Do not exaggerate your claims. If you do I promise you will regret it. Finally finish with your demand. Good luck.