The blue flare within the skull of the Skeleton Solider was known as Dead Flame.
Dead Flame was like a life source for any dark being, and to kill any dark being, diminish this Dead Flame was the key.
The Dead Flame was quite frail, and as long as it was touched by any weapon or exposed to the air, it would diminish. But it was only the earliest form of Dead Flame because Dead Flame is only found in Dark Being without any magic power.
If a Dark Being had awakened magic power, the Dead Flame would be encased on the Magic Core. Unless someone could remove that Magic Core or destroy it, the dark being won't die easily unless they got completely obliterated!
As for those Extraordinary Tier Dark Beings, their Dead Flames were even more difficult to sniff out because the higher tier a magic core, the more difficult it was to destroy it. Even if Dark Beings lost their limbs, they could continue to fight as long as the Dead Flame wasn't touched.