Putin hates Hillary because she realizes we're in a second cold war. She was in favor of a much more aggressive foreign policy than Obama. That means sanctions and placing US troops in our NATO allies + expanding NATO into the Baltic to protect Ukraine and Belarus.
There are a bunch of reasons the GOP has for hating Clinton, but fundamentally the GOP hates as a means of attaining power. The Republicans have defined themselves as in opposition to the modern world in some vaguely defined notion. This is precisely why they are incapable of governing: they have no policies other than 'not the Democrats.' Even Mitt Romney in 2012 said his economic policies were 'What he said but better,' and Mitt is 3 orders of magnitude better than most of these schlubs.