It is hard but it is also fun to get it. Follow all the above advance. Also use your dead enemy kit. When you kill them, pick up their kit. If they are supply or medic, you can drop the box. Then pick up back your own kit on the floor. You can stand there to heal or resupply yourselves.
Most of the time, people choose to be Support to defend their titan.
Back to the day I get that Badge, I join a 6 people server. I get to enemy ship once the shell is down. I RDX the first 2 consoles, use enemy kit to resupply myself. Then RDX the other 2, kill the 2 defender, resupply again then RDX and gun down the core. I get the Destruction Badge and problem solving pin together.