Costin, of Coldridge Drive, separately accused three men of rape attacks and a fourth of physically assaulting her in her own home.
London’s Appeal Court heard one of her victims was able to rubbish her claims with a “cast-iron alibi”.
He was away on holiday at the time when he was alleged to have attacked Costin, said Lady Justice Hallett.
All three men accused of rape had to undergo intrusive medical examinations, and one of them was particularly vulnerable due to his mental state, the court heard.
Costin’s false complaints were levelled against her victims between January and March 2016.
She told police that one of the men raped her on the carpet of her own home after first taking off her clothes.
The man was arrested but rapidly released when police confirmed his alibi, said the appeal judge.
But, soon afterwards, Costin made another complaint of sexual assault against the same man, claiming he had grabbed her breasts.
He was arrested once more, but again released after providing a compelling alibi.
Costin’s second victim was similarly accused of raping her at her home, the court heard.
She lied that he “forced her onto the sofa, and pulled down her clothes and raped her”.
Police were able to confirm that he was at home watching TV at the time, but Costin responded by making yet another false rape complaint against him.
This time he was able to prove that he was eating a takeaway dinner at home at the time.
Costin’s other offences followed a similar pattern, said Lady Justice Hallett.
Her case reached the Appeal Court as lawyers for the Attorney General, Jeremy Wright QC, attacked her sentence as “unduly lenient”.
Lady Justice Hallett, sitting with two other judges, noted Costin’s “extensive history of mental health difficulties”.
But she also highlighted the “insidious” nature of her crimes, which had a deeply traumatic impact on her four victims.
In letting her walk free, the Crown Court judge “placed too much emphasis on her problems and difficulties, and insufficient emphasis on the consequences for the victims and for the criminal justice system”, she added.
Lady Justice Hallett substituted a four-year prison sentence for the community order.
Costin was ordered to surrender to police custody in Shrewsbury by noon today to start her sentence.