I'll give it a shot:
命がけで = "risking one's own life." 命, as you likely know, means "life," and I believe the がけ comes from the verb 懸ける, meaning "to put (something important) on the line." Thus, 命がけ refers to "putting one's life on the line." When you add で it becomes "by putting one's life on the line." 命がけで守る is "to protect by way of putting one's life on the line." 価値があるのか is asking hypothetically "is there the value?" Put it all together and we get:
"この世界は、命がけで
守る価値があるのか。。。?"
Literally:
As for this world, does value to protect with one's life exist...?
Loosely:
Is this world valuable enough to risk one's own life protecting...?
Makes sense to me, anyway. Hope that helps!
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