To do something about this!

[Uhuhhoney]

My flatmate is from Lithuania. Very educated scientist but struggling to get work here. Shes lived here 5 years. She works part time and ive just found out her boss pays her 30 quid for a 12 hr shift.

How can i help her?

That's disgusting! There are plenty of legal and HR people on here who'll be able to help, so I'll bump this for you.

Does she have a decent cv?

Here it recommends you phone ACAS.

Does she have the documents to prove she can legally work in the UK?

I would be looking to get her into any job where she'll get the minimum wage.

Why is she struggling to find work? As an EU citizen she is just as eligible as anybody else to work in the UK. Is it poor language skills? Or the area you live in? Or some other reason?
In any case, for starters you could/should: make her aware that her employer is breaking the law; inform her of national minumum wage legislation; encourage her to report her current employer to the relevant authorities and to contact CAB as regards claiming back the pay she is entitled to. AND, perhaps most importantly for the future: help her to find and apply for jobs that pay at least NMW.