Sorry to hear of your problems.
First of all my advice would be DONT BUY THE FLAT You would then be stuck with it and even if your neighbour moves out you could end up with another tenant neighbour from hell. To have a bedroom on one side of a Party Wall and a lounge on the other is just poor design.
You ask whether you should contact the NHBC and you must do this as soon as possible. The Buildmark warranty is valid for two years. You should however, first write to the house builder and copy the letter to the Housing Association. Don't worry about upsetting the builder, they caused this problem and your other defects! Hopefully they will be as helpful again.
It is good the flat was Acoustic tested, some of the builders hide behind the "Robust Details" for sound insulation and therefore do not have to have a test for sound insulation. However the NHBC may decide that as it passed the test there is not a "defect" It will depend on where exactly the test was carried out. I would strongly suggest that the Housing Association get the house builder to pay for another sound transfer test. It would also be a good idea to look inside the cavity of the wall at your bedroom if it is masonry with a fibre optic camera.
Common reasons for sound transfer are:
Holes or gaps in the dividing wall, mortar joints, floors etc.
Cavities not filled with mineral wool sound insulation at each end allowing flanking sound.
Wrong type of materials being used, wall ties, blocks, plasterboard.
Cavity bridged with mortar allowing sound waves to pass through.
Finishes and structure not isolated. ie other Robust Details not being followed.
If the Party Wall is Timber Frame then sound transfer may not be the only problem. It may not have the required fire resistance too if a layer of plasterboard has been missed or the incorrect plasterboard has been used.
Finally it is possible that the wall was not inspected or inspected properly/thoroughly. There are not enough NHBC inspectors to make all the required inspections, so it is true the wall may not have been inspected.
I hope this helps but it will be down to you and your determination to keep complaining.
If all else fails there are laws to stop neighbours being noisy so you could contact your local council, buy be aware this could further antagonise your neighbour!