There is somewhat less dramatic version -- "держаться изо всех сил" ("clinging on with all your strength")
Clinging on for dear life to the side of a vertical cliff, the tiny lion cub cries out pitifully for help. -- Изо всех сил вцепившись в отвесную скалу...
That's more like "cling TO life".Цепляться за жизнь.