From Longman Dictionary of Contemporary Englishmake headwaymake headwaya) PROGRESSto make progress towards achieving something – used especially when this is difficultmake headway towards/in/with etc Foreign firms have made little headway in the US market. b) FORWARDto move forwards – used especially when this is slow or difficult Stormy weather stopped the ship from making headway. → headway
Examples from the Corpus
headway towards/in/with etc• Labour has not made headway with that point.• Achieving a standstill is vital for Heron if it is to make headway in rescheduling its debt. 