一目散に as fast as one's legs can [would] carry one●as hard as one can lick●like a scared rabbit

一目散に逃げる betake oneself to one's heels●flee in all haste●flee like a bird〔【語源】詩篇、11:1〕●head for the hills●run away at full speed●run for dear life●run for one's life●run like a rabbit●run like a rat●show a clean pair of heels●show one's heels●take to one's heels and run (away) 【自動】skedaddle〈話〉

一目散に逃げ出す go into full flight●take it on the lam●take to one's heels [legs]