This trophy will be earned when you start incubating the Kubrow egg you obtained in Step 7 of the Tips & Strategies section. This is required as part of the quest. The issue many people will come across will be obtaining the Kubrow egg, it could even take you over 20 hours to try to obtain the Kubrow egg.
Update 15 trophies are all about a Tenno's best friend, a foaming at the mouth, vicious, yet adorable Kubrow.