"恰恰在那个时刻" can be translated into English as "precisely at that very moment" or "exactly at that instant".
Both expressions convey the idea of something happening at a specific, exact point in time, with a slight nuance:
"Precisely at that very moment" emphasizes accuracy and exactness.
"Exactly at that instant" focuses more on the immediate, fleeting nature of the moment.
Choose the one that best fits the context of your sentence.