I tried looking “silly” up but it was furtile - silly is not an adverb, but in those 2 sentences it is clearly an adverb (and it augments the meaning of the adjective “bored” and the verb “beat”)
Could you tell me if you’re familiar with this usage?
Technically I wouldn’t say that ‘silly’ in your examples is an adverb. It complements rather than qualifies the verb.
means you are so bored that you have become silly or stupid.
means I’ll beat you so hard that you will become silly or stupid. Incidentally our little friend the comma inserted here I’ll beat you, silly means I’ll beat you, you silly person. Back to your original point then - ‘silly’ is an adjective. The adverb form would be ‘sillily’ but we don’t use that.
I also think the word ‘silly’ underwent a sorry meaning change because in the long distant past it meant innocent/harmless even happy or contented. In fact there are some islands off the southwest coast of England that are called the Scilly Isles, where the old meaning persists - but I digress.
Just one final point - the word you wanted was futile.