First, give them a backstory that ties into the RWBY universe. For example, they could be from a family that has a history with Grimm research. Second, give them flaws. Don't make them all - powerful. Maybe they are afraid of the dark because of a bad encounter with Grimm at night. Third, have them develop relationships with the existing characters. If they are constantly butting heads with Yang because they are too reckless, it makes them more believable.
A believable self - insert character in RWBY Grimm fanfiction should have a personality that is consistent. They can't be all sunshine and rainbows one minute and then a cold - blooded killer the next. Their reaction to Grimm should also be in line with their character. If they are a pacifist at heart, they might try to find non - violent ways to deal with Grimm at first. And they should have a growth arc. Maybe at the start, they are timid around Grimm, but as the story progresses, they become more confident and capable of handling them.
To create a believable self - insert in RWBY Grimm fanfiction, think about their motivation. Why are they in this world? Are they seeking power? Revenge? Or just trying to survive? Also, consider their appearance. If they are from a different world, their style of dress or their physical features might be different, which can cause some interesting interactions. And don't forget about their skill set. If they are new to the world of RWBY, they might not be as skilled as the main characters at first and have to learn.