against the odds

亡くなった女性のためにも一刻も早くこの酷い状況を改善してもらいたいです。
India files murder charges against suspects in brutal gang rape
New Delhi (CNN) -- Indian authorities added murder charges Saturday for suspects in the brutal gang rape that led to the death of a 23-year-old woman and sent outraged protesters to the streets.
The suspects already faced rape charges.
Six people, including a minor and a bus driver, have been arrested in connection with the rape that occurred in New Delhi this month.
Throngs of people have protested for days, demanding more protection for women and punishment for those behind the assault.
The woman was airlifted to Singapore earlier this week after she was treated for injuries in a New Delhi hospital.
Singapore doctors said she died "peacefully" early Saturday, surrounded by her family and Indian embassy officials.
The woman had been in "extremely critical condition" since her arrival Thursday and took a turn for the worse, said Dr. Kelvin Loh, chief executive officer at Mount Elizabeth Hospital.
"She had suffered from severe organ failure following serious injuries to her body and brain," Loh said. "She was courageous in fighting for her life for so long against the odds, but the trauma to her body was too severe for her to overcome."
http://edition.cnn.com/2012/12/29/world/asia/india-rape-victim/index.html?hpt=wo_c1

oddsは「(優劣・善し悪しの)差；優勢、勝ち目；(競技で弱者に与える)有利な条件、ハンディキャップ」、「見込み、可能性」（『ジーニアス英和辞典　第３版』大修館）という意味を持ち、against (all) the oddsで「強い抵抗[大困難]にもかかわらず」(ibid)という意味になります。Weblio辞書には「予想に反し」と載っていました。
またTheFreeDictionaryに"if you do or achieve something against all the odds, you do or achieve it although there were a lot of problems and you were not likely to succeed"とあり、「（物事などを）達成できる見込みが低い中で」というニュアンスが含まれているようです。

非常に厳しい状態の中でも必死に闘っていたのですね。ですが外傷は酷く、打ち勝つことはできませんでした…。
このニュースを読むまで、インドで女性に対する暴行事件が多発しているとは知りませんでした。２度とこのような事件が起こらないよう対策強化をしてほしいです。(Hatahata)