It's hard to say for sure. If the fanfiction focuses on Hinata's growth, she could potentially defeat Pain through her own skills and some unexpected twists. But Naruto is also likely to be a major factor, so it could be a combined effort of both of them that overcomes Pain.
In this fanfiction, Naruto might be extremely enraged seeing Hinata in danger against Pain. Hinata, on the other hand, would likely show her newfound strength and determination. Maybe she'd manage to land a few surprise attacks on Pain before Naruto fully jumps into the fray.
The outcome in this fanfiction could be a draw. Naruto and Hinata would put up a great fight against Pain. Naruto would be all fired up, using his Rasengan and other ninjutsu. Hinata would be there, protecting Naruto's blind spots with her gentle fist techniques. But Pain is no pushover. His ability to control gravity and rain down destruction could keep Naruto and Hinata at bay, leading to a situation where neither side can fully defeat the other.
One possible plot twist could be that Hinata discovers a new power within herself during the fight against Pain. Maybe she can tap into some ancient Hyuga ability that even she didn't know existed. This new power could turn the tide of the battle and surprise both Naruto and Pain.
Hinata would probably be extremely shy at first. She might blush furiously and be at a loss for words. After all, she has had a crush on Naruto for a long time, so it would be a dream come true for her.
She might immediately go to comfort him. Hinata has always cared deeply for Naruto, so seeing him cry would likely trigger her protective and empathetic side.
The 'jiraiya vs pain' in RWBY fanfiction could be a battle of wits as much as a battle of powers. Jiraiya is a very experienced ninja, and Pain has his own ideology - driven powers. In a RWBY setting, the battle could be affected by things like Dust, the special energy source in RWBY. Jiraiya might be confused by this new element at first, while Pain could try to incorporate it into his attacks. It would be a clash of two different power systems and fighting styles.
Hinata might react with anger. She's a strong - willed character deep down. So she could confront the person who cheated on her head - on. She might yell and express her disappointment and hurt. This would show her growth from a shy girl to someone who stands up for herself.
The biggest difference is the creativity of the fanfiction writers. In the anime, the fight follows a set storyline. But in fanfiction, anything can happen. For example, Naruto could suddenly gain a new power that was never in the anime. It's like a whole new world of possibilities.