Korra (both show and character) was very popular even when we only had one piece of concept art that didn't even show her face.
Season 1 premiered to an audience of over 5 million viewers.
While the show did lose viewership during its run (mostly over the course of seasons 1 and 2,) it retained a lot of popularity up to its series finale.
It was pulled off the air in the middle of season 3, but the official reason isn't because of poor ratings (it was still breaking one million viewers per episode, even when 4 episodes from season 3 were leaked online before S3 had an airdate) but because Korra pulled in massive numbers for Nick's website and they decided to keep it there. Season 4 was entirely online.
Korra herself was also popular but not always in the good way. She divided a lot of fans during season 1 and even more so during the first half of season 2. Season 3 and 4 is where most of her praise comes from, seeing as how there's real effort to give her development and good character there.