Fig.: to want something very badly; to be ready to go to extremes to reach one's goal

Why all the nasty vitriolic comments on the famous actress wearing a bikini shortly after having a baby and showing a non-perfect body. How unkind! A lot of women would give their eyeteeth to look like that in a bikini

Non capisco i commenti al vetriolo solo perché la famosa attrice indossa un bikini poco tempo dopo aver partorito e mostra un corpo non proprio "perfetto". Che cattiveria! Un sacco di donne darebbero non so che cosa per poter indossare decentemente un bikini

The young mother would give her eyeteeth to see her son grow up healthy and happy in a world without war

La giovane madre darebbe dieci anni della propria vita per vedere crescere suo figlio sano e felice in un mondo senza guerre

The eyeteeth - which according to someone got this name because their nerves are closed to the eyes - or canines, are very important teeth because they are used for both biting and chewing. Therefore, being ready to sacrifice such an important part of your body for something, it means that this thing is extremely important for you