I can't seem to beat the final case where Max is on trial against his father...

Obviously exactly what skills you'll be able to use depends on what you've unlocked, but what worked for me was ignoring Max Sr and taking out the other opponents until they'd been replaced with a weak combination I could safely leave there.

For example, I ended up with a couple of witnesses with maximum damage 3 and a couple of witness protection guys. At that point I switched to attacking Max Sr, using 3 Courtroom Dramas per turn to reduce my incoming damage to zero and the rest of my action points to attack. Don't attack the other opponents once you've got a safe combination, since they'll just get replaced with something stronger.

If you don't have Courtroom Drama you'll probably have to spend a few more action points each turn to negate the incoming damage, but you should still be able to do so and having something left over to slowly attack the boss.

Don't attach senior initially, build up a list of low scoring witnesses and evidence. Get rid of the witness protection guys and then attach senior. It took me eleven rounds to wear down his score, but it was worth it

Make sure you have the intimidate skill. He even references the skill when you use it. Then keep the low damage witnesses/evidence and start attacking your dad. I beat it in about 4 or 5 rounds

You should keep the 1-2 damage witness/evidence
In my case I got only attacked by 2 witness with 1-2 damage and 2 witness defende
Then I finish every round focusing on attacking the dad (I suggest use the 50% less credibility first)
Takes me only 4-5 rounds to win

I can't believe I actually did it in 3 rounds... The most important abilitiy I used was "intimidate" to lessen his credibility with 50%. I did this in the first round, then "objection" for him to not add any more opponents in the next round. Then I took out the most damaging witness and the evidence. Since I had 1 action point left I used "great posture" to ensure I wouldn't lose because of lack of case strength. In the next round I used "swagger" for more action points, and then I spend it all on "tirade" which will lower his credibility with 24. Then the next round all I have to do is take out Max' father with those basic abilities, cause all the credibility he has left is 6. Bam!

This will be a detailed answer and for my strategy, you did need to unlock some high end abilities.
You don't necessarily need to use my strategy to win but it might take more rounds to win without having certain high end skills. Intimidate is a really useful skill to have that makes the whole game easier (I didn't unlock this at all though) and Great Posture (the final ability in vanity) really helps in this final battle.

I had unlocked the 'Great Posture' Ability in the Vanity section and I used this ability in my strategy to beat Max McMann Senior.
I first eliminated opponents with high damage (eliminated the second witness and the evidence in Round 1)
(Detail: I did have to repeat Round 1 to eliminate the witness with cross examine as sometimes it doesn't produce enough damage to eliminate).
I then used the damage reduce actions (mesmerise) on the leftover opponents that cause damage.
I kept the Witness Protection and I kept the one Witness with very low damage (1-2).

In Round 2, got a new witness with high damage who I eliminated using the Cross Examine ability.
Also got a new evidence with very low damage (just 1), keep this one.
I then used the Great Posture ability.
This would allow me to recover from the low damage attacks from opponents in future rounds.

I then used the Deep Voice and Ego Boost abilities so I could use it on Max Sr. If you didn't have Ego Boost, you can still win but it will take more rounds.

In Round 3, I got a new Witness Protector - I now had 2 witness protectors and 2 low damage opponents, now since my Great Posture ability was recovering the attacks from my opponents I didn't have to do anything else to opponents.

From this point onwards, you can use all your action points to attack Max Sr until he is eliminated and you win the game.