To do that you need to be a good hacker.
The best you can do now is to block the number on whatsapp and also on your phone.
If he/she calls with a different number, pick the call and record what he/she says including text and whatsapp msgs and lodge a formal compliant to the police using those as evidence.
The most practical way to get information from a potential blackmailer is through social engineering
Social engineering is a type of hacking attack that relies heavily on human interaction and often involves tricking people into breaking normal security procedures.
You can actually pick the call and speak to the person, using psychology and other tactics, you can find more information on the attacker. You can even send him tricking msgs that are meant to confuse him/her.
Its the best form of hacking such situations.
The most important factor in threats is to induce fear. You must never become fearful due to the threats.