If you can meet the requirements, it would appear to be fairly straightforward to obtain these records.
From Library & Archives Canada:
Records of immigrants arriving at Canadian land and seaports from January 1, 1936 onwards remain in the custody of Citizenship and Immigration Canada. To request a copy of another person's immigration record, you must mail your request to the under-noted office:
Citizenship and Immigration Canada
Public Rights Administration
360 Laurier Avenue West
Please note that:
The request should include the full name at time of entry into Canada, date of birth and year of entry. Additional information is helpful, such as country of birth, port of entry and names of accompanying family members.
Applications for copies of documents must be submitted on an Access to Information Request Form [www.tbs-sct.gc.ca/tbsf-fsct/350-57-eng.asp
] by a Canadian citizen or an individual residing in Canada. Fee: $5.00, payable to the Receiver General for Canada.
The request must be accompanied by a signed consent from the person concerned or proof that he/she has been deceased 20 years. Proof of death can be a copy of a death record, a newspaper obituary or a photograph of the gravestone showing name and death date. Proof of death is not required if the person would be over 110 years of age.