With my union hat on, I'd say fight and fight and fight. I did, and my union (UNITE) were brilliant. And I won, in that I got a shiny new role with a shiny nice new boss, and so I agreed to that.
BUT the old boss got away with it. She said sorry to her boss, but not to me. Tbf I'd never have believedd her anyway. And it was a sorry for the misunderstanding (mutual apparently!). Not for what she did to me. Nor for what she did to others in the past. Not for what she'll do to others in the future. You see, she's a bully. She's also not remotely good at her job. But she's popular with higher managers because she's great at appearing good and few people have called her out on it. The reason she hated me because I did.
So please believe me. Even if you go to a tribunal, and if you win it, or if you get a settlement, you will still be angry, you will still feel wronged, and whatever justice you think exists won't happen.
I may be wrong, I hope I am, but I'm going to say it anyway. If you want an apology, vindication or whatever, there is nothing in the world that will get it for you. You will possibly end up bitter, unable to move past it, and unemployed. None of those are great prospects.
And that is also what nearly every single member I have supported has said too. Many wouldn't do it again even it they won. I would, but only because I have no capacity to be a doormat - and I've wished I did at times!
Don't look for justice. Order your priorities practically - you almost certainly need a job and wage. That's what you need first, and if that's another job on the same terms with another manager, be careful not to let your pain or anger get in the way of being sensible. Your revenge is your escape, the fact that the manager knows you beat them, and so does everyone else. You showed everyone you'd fight back. And they'll think three times before trying it on you again.
Tribunals are dodgy. Most people lose. And remember that they don't exactly recommend you to other employers. Be careful what you wish for. Even if you get it, it may not look like what you expected. Tribunals should be last resorts. So should settlement agreements. Because unless they come with a job, they may not be what you wanted.