Great question. Initially, you may want to stick to challenging thoughts by looking at the evidence and the likelihood of it happening. Challenging a fear of death will take time and effort so you may want to hold off on this for awhile. Once you are able to challenge your fear of death it can be very freeing so it is certainly a worthwhile task when you feel ready. Search the forums using the keyword search as I think these conversations have come up before.
The fear of death can be challenged so let's explore this - if you were to die what would you do? How would you feel? How would you cope? Well likely you would not have to do anything and you would likely feel nothing so there would be no need to worry about coping. Likely the fear you experience now is much greater then the fear you would experience if you actually were to die. If you died that would be the end of fear. Some people use their religion as a comfort as well. How else do you think you can explore this fear?
I'm just about to start session 3 (challenging negative thoughts) having found the first two sessions really helpful - but am wondering how best to challenge negative thoughts that could be true? For example, I have a fear of flying and it's possible (though highly unlikely) that I could die in a plane crash. It's the possibility of this that makes me anxious, even though it's very remote. I still fly, but get nervous for months beforehand. How best should I challenge these thoughts?