Get a gold medal in the indicated campaign mission to unlock the Special Operation. 

Blastoff! (Special Operation 8)        : Campaign mission 15
Hostage Situation (Special Operation 7): Campaign mission 14
Lord of the Ants (Special Operation 2) : Campaign mission 9
Midnight Snack (Special Operation 1)   : Campaign mission 8
Road Block (Special Operation 5)       : Campaign mission 12
Sandy Breach (Special Operation 3)     : Campaign mission 10
Tan Some Hide (Special Operation 6)    : Campaign mission 13
This Old Fortress (Special Operation 4): Campaign mission 11