「一目散に」は
as fast as one can
as fast as one's legs will carry one
のように言えます。
例:
The pickpocket was questioned by a security guard and then he fled in the opposite direction as fast as he could.
「そのスリは警備員に質問されると、反対方向に一目散に逃げた。」
pickpocket 「スリ」
flee 「逃げる・逃走する」
The pickpocket ran away as fast as his legs would carry him after the security guard stopped him.
「そのスリは警備員に止められると一目散に走って逃げた。」
run away 「逃げる」
ご参考まで!