How do you handle aggressive tactics during negotiations?

One thing I always find helpful when aggressive tactics are being used is to take a break. Create an excuse to leave the negotiation, confer with your negotiation team on the side and then come back to the table later with a defined plan of how to move forward. Often just that break in discussion can diffuse the aggression. If not, then at least you have a path forward.

Never act on arousal (Economical Behavior research). You need to know your BATNA to see how to react in each point of the negotiation process.

I am certain that my background in Psychology, Mental Health and Litigation Law means that my capacity to be with the depth of emotion, angst and rage is greater as I practice meditation (with an extra t) and living in compassion when I am not mediating. I find such practice invaluable.

You should listen, but also set some boundaries. Usually (depending on cultures) being a passive listener is misunderstood as complying and accepting the terms that are being discussed, so you'll need to know perfectly well who and how you're going to negotiate with.

In mediation we have to be always actively listening which means really hearing what the parties are saying without commentary, judgment or trying to think up something clever to say. Of course there is managing discernments about what you might ask next or where it might go and the odd note taken, but the focus needs to be on the person speaking to be truly compassionate.

If someone is becoming aggressive and losing their sensibility which is common, the aggression needs to be met with a similar level from the mediator in order to facilitate their calming but it is important to let them rage enough to feel heard and to acknowledge and honour how they feel and think about the conflict. Summarising, rephrasing and softening what is said into more normal language is essential for ensuring the mediation is safe for all. Most important is how the mediator empowers the parties to self-express more easily in a way that the other party can hear because this is how the dialogue that leads to resolution is created.

Every person has a different version of what has happened so focusing on facts about events that form a part of the dispute is a mistake. Making the sums in dispute and key data agreed as facts between the parties is an important stage in mediation but even in commercial mediations, often the conflict has nothing to do with the data. To mediate properly the focus is on what the conflict means to the people because its the underlying values, interests and needs that matter more than any fact or piece of data.

There is no point in discussing solutions until the people are ready and they won't be ready unless they feel they have spoken, been heard, expressed what matters to them and explored what the dispute is about for both themselves and the other side. This is why mediation is so much better for solving disputes than negotiation and if properly mediated this way does not lead to further dispute. When tension rises that is the clue that that person has not had sufficient time to express and figure themselves and the other out to be able to understand the solutions that might be doable.

Postpone. If you see the meeting is going nowhere, there's always a chance to schedule a later meeting within a reasonable timeframe. Probably, the discussion might get a little "colder" in a couple of weeks.