According to the Hawaiian Dictionary, there is no Hawaiian equivalent for the superlative ("-est") other than "loa" or "nui loa". What you could say for "He is the biggest", then, would most likely be ʻo ia ka nui loa, using "nui" as a noun. In fact, the translation of the Hawaiian Bible uses this phrase in Matthew 18:4.
You could also say ʻoi loa kona nui, meaning "his bigness is superlative/the very best".
For "He is as fast as a cat", you need to use a verb sentence. You could use the English verb "like" to rewrite this sentence to read something like "His fastness is like a cat's". Coincidentally, the Hawaiian word for this meaning of the English verb "like" is spelled exactly the same.
We can use this Hawaiian verb "like" to translate the rewritten English sentence: Like kona wikiwiki ʻana me he pōpoki.
Like, of course, is the verb that tells us we're comparing; kona wikiwiki ʻana means "his fastness"; and me he pōpoki means "like a cat".
I am unsure how to translate the comparatives in the other direction.