Judging by the break-neck speed the manga is churning out the characters and their backstories, we're probably not going to get the rest. Elrise recalls her as a sub-heroine. Anyways, Elrise herself explains her version of the character where instead of her father losing the position of first knight, when he was in that position he criticized and advised Pizzarise and for his trouble was executed and had his family destroyed. In Elrise's memories, Aina would go on a revenge plot to try and kill Elrise. If the player doesn't interfere, she is stopped and then executed, but if the player does, then they elope and go on the run.
Then there's current Aina. Manga also skimps out on a few details. On top of the 4th place comment she was also hounded by the fact because she left early she didn't participate in the battle against Poochi and could constantly hear people going on about that fact. The novel also goes on to explain that growing up, Aina had extremely high pride that her father was the first knight and care taker to Elrise and would often use that look down on others. When she lost at the tournament, the comments would turn to "Hey, isn't her father the previous first knight? I guess somethings don't get passed to their kids huh (laugh)" which drove her mad. So yeah, her previous demeanor ended up causing her to become isolated which made her easy pickings.