I have come across it in this video. It is at 25 second. Here it is in context:
Animals come in pretty much every colour, but blue seems to be the rarest. What is cool, though, is when we find blue animals, they are awesome looking. Nature doesn't do halfway with blue.
What I can uderstand is that nature doesn't favour blue, but I cannot quite get the phrase itself.
To do things halfway means to leave the job or task unfinished, to fail to do much that was necessary or expected. Compare "to take half measures".
You could say of a person who threw a party, say:
It was quite a bash, with live music, lots of food, and plenty to drink. Dmytro doesn't do things halfway when throwing a party.
The speaker in your video is then deriving a new phrase from that familiar locution, patterned after another locution. See this question. Only here, it would be do + preposition or do + adverb (depending on how you analyze "halfway").
Nature doesn't do halfway is like saying of a guy who always drives his car too fast:
He doesn't do "slow".
And with means "with respect to, regarding, involving".
With regard to blue (creatures), it is not in Nature's nature to do anything other than a bang-up job.
