I think :
I'll do it no matter what will do.
But I relly need more formal alternatives, so can these work well:
I'll do it at any cost.
// // // at all costs.
// // // whatever happens.
// // // whatever the consequences are.
As far as more formal versions are concerned:
I'll do it regardless of the consequences.
I'll do it no matter what the potential outcome.
Note: If you are required to be extremely formal, then don't use the contraction "I'll", use "I will".