I don't see any no-win, no-fee solicitor taking on a case like this. The no-win, no-fee solicitors tend to only take on the cases where the have a >50% chance of winning. Otherwise, why bother.
The basic jist of it is that AIB have a signed contract on you agreeing to a rate. If what you are proposing were feasible, would a person who opts for any variable rate today not be able to take the same route if interest rates rise and they're no on the fixed rates currently available on the market?
I suppose you could arrange a meeting with a no-win, no-fee solicitor but, in my opinion, it'd be a wasted half hour for both of you.