Because Digimon Tamers is my favorite show, I'd like to recommend that. It's got an amazing plotline (ending with a totally unconventional villain): The three main characters meet their partners and set about stopping any digimon who materializes in the real world, until they get caught up in something much bigger.
It has great character development for all main characters and in particular I feel it portrays the INTJ personality really well. I once complained here that INTJs in mainstream media seem to be pretty nasty characters in real life- that they're either villains or anti-heroes, and MOST are male. And on top of that, they're hard to relate to for me. I'm not average by any metric, but in the end I'm still not any sort of superhuman (and neither are most other INTJs), and many INTJ characters are written like that.
The show has a great female INTJ character: Ruki Makino. She's intelligent (Grand Prix winner), fiercely individualistic and snarky. She faces a lot of issues that INTJ females confront- she doesn't conform to most of society's expectations of a female, and doesn't get along with most people in society. Her mother is a model and constantly tries to mold her daughter in her own image, which caused her to rebel, and in the anime mother and daughter initially seemed to be reluctant housemates. Her mother doesn't really know what to do with her, and she comes and goes as she pleases. Generally, she's just very independent.
Like I was at that age (she's preteen), she looks down on any form of sentimentality and was extremely cold in her dealings with her partner digimon. She was also cold to the other two characters and tried to destroy their Digimon because her belief is that digimon only exist to destroy each other or be destroyed. Needless to say during the show she develops her Fi and learns how to make friends. Before the end her relationship with her mother also improves dramatically, as both learn to understand and accept each other. I find her development to be very realistic as I can see many of the same changes in myself as I aged (except she does it in the space of a couple of months, while my development too YEARS)
Her PARTNER, Renamon, seems to be INTJ as well. These two are nearly telepathic with each other.
This is, in my mind, how more INTJ characters should be written: neither an antihero or a villain, and certainly not always a mastermind genius. But simply an individual with problems of her own, and a rare personality that not many people can understand.
I would go for the Japanese version with subtitles than the English version...