Justice and The Law
Law often says in cases like this, where an offer of settlement exceeds the amount of compensation awarded, the claimant is responsible for costs of trying to get a better award than they were offered; they incurred the additional costs of both parties on a gamble that did not pay off. And if that is the case it seems she doesn't have a leg to stand on.
The specific problem in this case is she had legal costs ($224K) which exceeded the offer made, but that is not the defendant's problem. Their offer ($85) was generous set against the court ordered award ($18K) and the court has to recognise that. The defendants spent money saying that she shouldn't have got more than they offered and the judge agreed so why should they pay the cost of proving that; they won that part of the legal battle and the loser pays costs.
How she ran up legal costs so high before the offer is a bit of a mystery and it seems they will go higher if the appeal is thrown out and I would guess it will be. I have seen people misled by solicitors promising things which would never be delivered and this may be a case of that or maybe their client is instructing them to continue despite being told it's largely hopeless to do so.
It's an unfortunate case but she won't be the first to have been caught out through over-optimism. If it was on the basis of bad or flawed legal advice she may be able to take her own solicitors to court. Unfortunately in cases like this it means spending ever increasing amount of money and still with no guarantee of coming out ahead of the game.