Remember that this is perhaps the most defining moment of Biff's life. It is the discovery of his father's adultery that sets Biff on the road of becoming an itinerant worker who drifts around without any seeming aim or purpose in his life. Therefore it is going to be perhaps one of the most important events Biff could write about in the diary you have been asked to complete.
If one looks at the scene in Act Two, one can see the sense of betrayal and shock that Biff feels when he discovers the truth about his father. Note the following exchange and how it introduces a very important symbol that runs throughout the play:
WILLY: She’s nothing to me, Biff. I was lonely, I was terribly lonely.
BIFF: You—you gave her Mama’s stockings! [His tears break through and he rises to go].
The symbol of silk stockings is used throughout the play as a symbol of betrayal, and what is interesting about this quote is the way it shows that Biff focuses his anger on the stockings rather than on his father, seeing the silk stockings that Willy had promised Linda but actually gave to the Woman as the ultimate sign of his betrayal. It is this event that causes Biff to think of his father as a "fake" throughout the rest of his life.
Any diary account from Biff about this event must therefore capture the sense of massive betrayal and disappointment that Biff would have experienced. Remember he looked up to his father as if he were a god. Now, that god has been toppled from his position of dominance and Biff has to cope with his father's flaw. You will need to communicate anger, frustration and immense disappointment in your account, as well as indicating how this discovery impacts Biff's future life decisions. Good luck!