That birth certificate says that Alexander was aged 33, and born in Boleskine.
Boleskine is on the east shore of Loch Ness, in the county of Inverness, not Ross and Cromarty.
There is a baptism of Alexander Mackenzie, son of Colin Mackenzie and Anne Mackenzie, on 30 January 1822 in Boleskine, who would fit. However you'd need to find evidence to prove that he's the right one, as there could be another one whose baptism record hasn't survived.