In English law the prosecution have to prove their cases beyond reasonable doubt. The defence technically don't have to prove anything, although it helps their case if they do. The burden of proof is always on the prosecution though.
Which makes this case tricky as what seems to be missing is clear cut proof she did the things suggested other than her being around / volume of incidents. It'll depend what the jury make of that.
Also each count is distinct i.e. she could be found guilty of some and not guilty of others.
We haven't heard from the defence yet and I'll be interested if Letby takes the stand or not. She doesn't have to.
Seen a few mentions of UK law - Scottish law for one is different as they have 3 verdicts and can deliver a 'not proven' verdict.