I think "contra las cuerdas" means "in a hard/difficult place".
Poner contra las cuerdas (a alguien) = to place (someone) in a difficult position / to pressure someone / to make things difficult for someone
Estar contra las cuerdas = to be in a tight spot / to have problems
Edit: It looks like the movie
Against the ropes it translated
contra las cuerdas. So that is probably the most accurate translation, and this expression must come from boxing terminology.