Depending on context, these terms could be used to challange, to provoke.

There can be many explanations.

As mentioned by you, this small phrase has multiple shades of meanings. I have tried to capture some of these.

Himmat hai to bhiRkar dekho = Just try to fight with us if you have got courage or guts.


OR

ZarA hum bhi to dekhen tum kis khet kii moolii ho = Let me see, what your calibre or might is.

Or

Hame dhool chatAne kii koshish karke dekho, hum do-do hAth karne ke liye taiyyAr hain = "just try to beat us; we're ready to rumble". This Hindi sentence contains two idiomatic expressions.

OR

ZarA hum bhi to dekhen ki tumhArii mA(n) ne tumhe kitnA doodh pilAyA hai = This is yet another stylish way of saying "show me what you've got."

In the field of marketing, It can be written as
‘Show your potential’ & in Hindi it can be written as
(Aapni Xmatayon kaa pradarshan karo) अपनी क्षमताओं का प्रदर्शन करो
If we want to offer a challenge, then it would be
(Aao Jor Aajamayan) आओ ज़ोर आजमायें

आओ देखें तुम्हारे बाज़ू में कितना दम है

One more natural expression to challenge someone.