I'm not going to make any comment about what is said on any other forum. I stand fully prepared to be corrected, but I believe anyone offering a 3 day service is a tout looking to suck people in to going with their chosen lawyer, who will start making excuses as soon as the money is paid.
Every comment about times frames and offices closing early is based on what happened to me personally, not what I read.
I stand by my comments, 5 working days if all the planets align and 6-8 working days if they don't, and reality cuts in. 6 days is relatively easy to achieve, with an extra 2 for contingencies, or if less than breakneck speed is desired.
Here is a 7 day schedule I did for a friend (May 2013) to use without a lawyer. It is reasonably relaxed and includes a mixture of private and public medical checks. It does not include the double legalization of the Interpol and Residency certificates, because I only required that for my cedula. The rules may have changed and Migracciones may now require them, or it may be just a cedula thing, I don't know. Using a lawyer, or more specifically, their driver, who can do some running around dropping stuff off and picking stuff up, will speed things up, but other things like test results and some certificates just take time.
Day 1
Migracciones
Pick up checklist of up-to-date requirements
Ministerio de Salud
pick up health adjudication form
pick up list of health tests required
make appointment for psych exam
Escribania
Declaration stating that you agree to abide by the laws of Paraguay.
Certify 8 copies of passport ID page
Certify 4 copies passport Visa and Entry page
Certify 1 copy of Birth, Marriage, Police Certificates
Translator
Drop off Certified copies of Passport, Birth, Marriage, Police Certificates
Photographer
6 x passport photos taken if required
Interpol
Submit application
Your Hotel
Obtain letter of residency
Obtain details of 2 native Paraguayos, Name, DNI, phone who are willing to tell the police you are known to them and reside where you say you do.
Day 2
Ministerio de Salud
Blood test
Ministerio de Relacciones exteriores
Drop off Passport to have Visa authenticated (if required)
Drop off Original Birth, Marriage, Police Certificates
Medical Clinic
ECG - private option
Ministerio de Relacciones exteriores (afternoon)
Pick up passport
Dermatologist
Dermatological Examination (private option)
Day 3
Ministerio de Salud
Certification of Private Doctors ID stamps
Psychological Examination
Yellow Fever Vaccination - if required
Ministerio de Relacciones exteriores
Pick up Legalized documents
Translator
Pick up translations
Ministerio de Salud (Afternoon)
Pick up certified private doctors certificates
Day 4
Interpol
Pick up documents
Escribania
Copy and certify Interpol certificate
Identificacciones - Policia Nacional
National Police Check
Day 5
Ministerio de salud
Pick up blood test results
Local Police Station
Life and residence certificate
Medico Clinico - Colon y Humaita
Adjudication of medical results
Day 6
Ministerio de Salud
Submit docs for Health Certificate
Nacional Banco de Formento (left to last in case of terminal problem)
Deposit ($5000.00 USD) or equivalent
Ministerio de Salud (afternoon)
Pick up Health Certificate
Submit Health Certificate for verification stamp
Escribania
Obtain 2 copies of all documents and have certified
Obtain Limited Power of Attorney so your lawyer can deal with Migracciones on your behalf
Day 7
Ministerio de Salud
Pick up verified Health Certificate
Escribania
authenticate 2 copies of verified Health Certificate
Migracciones (open 0730 - 1430)
Submit Application