"破釜沉舟" can be translated as "to cut off all means of retreat" or "burn one's boats," which means to commit fully to a course of action without any possibility of turning back.
"夸下海口" can be translated as "to boast excessively" or "to make an exaggerated promise," which refers to making grandiose claims or promises that may be difficult or impossible to fulfill.
Together: "Burn one's boats" and "boast excessively."