Once you have the Ronin Titan load-out. (Beginning of a mission with a giant Satellite dish is where you get it.)
Simply get your titan core ready to use and get a Titan to very low health (not the point where it has a count down to explode) then simply activate the core and use your melee attack. You can use the Y ability to jump towards the titan in question. I did it with the level boss for the level you receive it. It popped after they exploded.
If you've finished the campaign and not got it, witter56 made a good point:"A good mission to do this would be the Trial By Fire mission as there are many Titans you can kill here. Simply kill some Titans, let one of them drop their health to 25% or so and activate your Core."