No, no "cover letter"'accompanying the N-400 is needed or necessary. Just follow the "normal" steps.
Select "other" and type in the same "class of admission" you read on your green card, or simply type: "VAWA".
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
I agree with my Colleague, USCIS is well aware of the VTVPA amending INA section 3 19(a) which allows for VAWA applicants to apply for naturalization after 3 years of being a Permanent Resident.