This series basically take place in an alternate universe of the original Star Fox's universe where Fox was caught in the blast with Krystal hot on his heels.
It caused a splinter time line, but without a Fox in this timeline the same events leading up to the blast could not occur. Thus there are two time lines, one where fox was fast enough to escape the blast, and time continues as per normal and one where he was too slow, and reality adjusted, this is the Xero Chronicles timeline.
In this one Krystal, being close enough to be affected has been sort of forced into fox's mold, with backstory intact.

She is now the Son of the famous founder of Starfox an ace pilot. She can't very well be his SON if she's all woman.
She still has her original memories, and they won't fade any more than normal memories do. But she has all of fox's innate talent and skills, honed from years of physical training, as well as her own hand to hand and telepathic skills.

She'll slowly find herself adapting as this timeline's fox, but those memories won't fade, and nobody will believe her. Maybe it's just some insecurity about her gender... right? or maybe the trauma of her father's death that she's obviously still dealing with?

As far as her friends are concerned she's Krystal McCloud ace pilot, bounty hunter, mercenary, and hero who saved the system from distruction. She's got a thing for the cute girls and is sort of like original series han-solo.

Look for more tales of daring do with the heroic Krystal McCloud!