Negligence is still a better word of all synonyms because it is a legal term, a part of legal practice. You can shorten your phrase, instead of
negligence shown by a person in performing a duty
you can use legal terms
- neglect of duty
- breach of duty
The person accused of breach of duty will be defendant.
Consider this legal text:
Breach of Duty
A defendant is liable for negligence when the defendant breaches the duty that the defendant owes to the plaintiff. A defendant breaches such a duty by failing to exercise reasonable care in fulfilling the duty.
