Learn Spanish (Latin America): La mujer acababa de descubrir el chantaje. - The woman had just discovered the blackmail.

When expressing that someone "had just" done something in the past, you must use the imperfect form acababa + de + infinitive. If you used the preterite (acabó de descubrir), it would literally mean she "finished discovering" it, focusing on the end of a process rather than the recentness of the event.

Since this lesson is about past assumptions, how would I say "The woman MUST HAVE just discovered the blackmail"?

To turn this into a conjecture or assumption about the past, you would change the imperfect acababa to the conditional tense acabaría. So, La mujer acabaría de descubrir el chantaje translates to "The woman must have just discovered the blackmail" or "The woman probably had just discovered the blackmail."

What is the verb form of chantaje if I want to say "to blackmail"?

The verb form is chantajear. For example, if you wanted to say someone was blackmailing her, you would say alguien la estaba chantajeando.

If I wanted to replace el chantaje with the pronoun lo, where exactly would it go?