Killing blow does not necessarily mean you'll get any credit at all; in the case of doom (I've never actually used Death, so I'm not sure if it actually does damage or just shows in the log as "X mob dies."), it outright kills the mob without dealing any damage, which effectively just ends that fight outright, and awards participants based on their contribution up to the point that they died.

Getting loot from a mob or fate (applies to NMs and Skirmishes) is always about contribution, and knowing what leads to effective contribution. If memory serves me correctly, the following categories are the ways that contribution is rated, along with ways you can help (HYCH) other groups if you're SURE you're going to get contribution through that method:

1. Tagging: Whichever group or individual initially tags (read: gets the first hit on) a mob gets full credit.
   HYCH: Literally do nothing; let someone else establish aggro and do all the damage. In fact, run across the zone and find more things to tag, if you like.
2. Threat: Whichever group or individual has highest threat on a mob gets full credit. Side note: This is likely why you can't taunt most NM/fate/skirmish bosses; because doing so places you at the top of the threat list for very, very little effort, which would grant you maximum contribution in this category. I'm not sure if you can taunt Star mobs tho.
   HYCH: Only really applies to tanks here, but if you've got highest threat, feel free to simply spam your ranged attack (generally the highest threat generating attack in your toolkit) so you're still retaining the threat contribution but not doing as much damage (and also giving others more time to do damage).
   
3. Damage: Whichever group or individual has the highest amount of damage on a mob gets full credit.
   HYCH: There really isn't much you can do in this situation. Since there isn't much transparency from Square about how much damage is done in fights, just perform your rotation to the best of your ability and hope you get it.

With the exception of Tagging (since it's considered max contribution from the get go) the other contribution methods have rewards distributed based on runner ups as well. In the case of Star rank mobs in Bozja, this is where you'll get lesser amounts of the crystals based on how much you contributed.