I was injured offshore and I want to negotiate with the company myself without hiring an attorney. What's the best way to negotiate an offshore injury case?

The first suggestion would be not to negotiate the case yourself if it involves a serious injury, significant time away from work, or otherwise involves more than just a minor injury or a few days away from work.

Why?  Because you will be entering a war zone.  The company will have experienced insurance adjusters, insurance investigators, and lawyers working "behind the scenes" to try to make your case worth as little money as possible.  They know the "tricks" that can hurt your case and they will use them on you with a smile on their face so you won't even see it coming until it's too late.

The insurance adjusters, investigators, and lawyers for the company make their living negotiating cases like yours.  This will not be their first time to negotiate a case or the last. 

If your case is serious, you should strongly consider consulting with a Jones Act or maritime law attorney.  At the very least, you should try to talk to such an attorney (or, better yet, talk to a few of them) before deciding whether to try to negotiate your case yourself.  Most of the time, such attorneys will give you a free initial consultation.

If your case is a smaller one, involving minor injuries or just a few days away from work, then negotiating yourself may be more efficient and effective.  Here are some "tips" for negotiating these small cases yourself:

1.  Get a copy of the accident report;
2.  Gather together all of your medical records and bills;
3.  Ask to take statements from all witnesses;
4.  Type up a letter to the insurance company, include the accident report, medical records and bills, and witness statements.  In the letter, set forth your opening "demand" (your first settlement number) by multiplying your medical bills and lost wages by some factor you think is fair;
5.  Give the company a deadline by which to respond.  If they do not respond by the deadline, you know they are not serious about your case.

Good luck.