What is the translation for 打出頭?
出头 has three usages:


Its literal/narrow meaning is make public appearance. A synonym is the Chengyu 出头露面. Its extended meaning is stand out; show off.
It can be used as short for 出风头 which exclusively means show off.
It can be used as short for 出人头地 which means stand out among peers; become successful. For this meaning, 出人头地 sounds natural but 出头 sounds somewhat vengeful.


In your context, without having watched the movie, I think it is the third meaning 'become successful (in a vengeful tone)'.

打 can be its narrow meaning beat up, or generalized boxing; kong-fu, or metaphorical use one's abilities; struggle. Since it's a Bruce Lee movie I guess it's a mix of the 2nd and 3rd meanings.

So as a whole, 打出头 means Struggle and successfully avenge using kong-fu.

Side note: those words and meanings are not exclusive to Cantonese, they are the same in Mandarin, but the formality is different. In Mandarin those words are considered colloquial and in the past it might not be formal enough for a movie title. In the recent years however, movie titles have become less 'literary' and anything is accepted. Admittedly this is a controversial topic that native Cantonese speakers may disagree; I am only speaking from my own perspective as a native Mandarin speaker from Northern China.