Restructuring/Debt Advisory

Restructuring is very technical and rule governed so I don't think they will expect you to have any real experience going in for this reason (and I know that a lot of places will sort of ease you in for this reason i.e. some generalist work beforehand). I would just make sure you can show definite interest and be able to speak about deals, different types of bankruptcy protection, distressed debt investors, etc.

For the debt advisory side, this is a more generic and repeatable service, so you will likely be expected to know a bit more about the process of debt advisory (either loans or bonds). Prior experience is more feasible in this department, be it through a bank's corporate lending practice, a credit rating agency or bank so may be more of a requirement in debt advisory than restructuring, so perhaps you could leverage any prior experience in this department or aim to get some experience before applying.

Lastly, as to your BB application comment - it is my understanding that BBs do not have strong restructuring practices as law dictates that you cannot advise on a restructuring if you have advised that company on an underwriting over the last X number of years. As underwriting usually involves a large syndicate and the BBs due it rampantly, that makes it very difficult to get resturturing mandates. Thats why companies like HLHZ, BX, Rothschild and Evercore are so dominant in the space despite the size difference