100% WRONG. The lawyer you contacted has NO idea. Here is what you do: IF you have someone who can do this on your behalf in Mexico. If you do not have someone to get this paperwork on your behalf, then you have no choice but to go the via the Canadian Embassy in Mexico and wait for whatever time it takes them.
1. Go to a fingerprinting agency and get two fingerprint cards. I used F1 in Mississauga. NO need to get it re-certified or translated.
2. Get a right side perfil & face picture taken 4.5 x 3.5cms colour, no makeup, no eyeglasses, earrings etc. (2 copies of each)
3. Write a letter authorizing someone on your behalf to do all that is necessary in Mexico to get you the certificate. See post #236 in this thread, the letter is there, in Spanish and you can copy paste. Two witnesses will have to sign the letter along with you. The person in Mexico you are giving the authority to can sign the letter when he receives the documents in Mexico. Make sure you also attach copies of their ID's front and back. A Canadian driving license will do.
4. The person in Mexico will have to make a deposit for MXN 178.00, @ "Banco Mercantil del Norte", S.A., Institución de Banca Múltiple, Grupo Financiero Banorte, a través del convenio 149583 y referencia 18443101
5. You will have to get your Canadian proof of address translated from English to Spanish and include the original of the translation in the package.
6. Copy of your passport, the main page and any other page with relevant information.
7. Copy of your birth certificate, translated to Spanish by a certified translator. I use
https://www.taontario.ca/, if you do not have a birth certificate your embassy can issue a certificate of birth, and once translated, that will work as well.
8. Letter requesting the Constancia de Datos Registrales. This will come to you via email from the Canadian Embassy in Mexico City.
The person you authorize needs to take all these documents to the local PGR/FGR office along with his original IFE/Passport and a proof of address. Once submitted, you will get your letter in about 10 - 12 days (it will be given to the authorized person). If you need any further help send me a PM