After the scene, head to the QCPD lockup. You'll find the militia and thugs you sent there while you're completing some of the missions. Continue inside and talk to Ivy. You now need to head to the Botanical Gardens as instructed by Ivy. Also, Bleake Island will have another threats like airborne quadcopters, a militia watchtower, and explosive devices you haven't disarmed yet.
On your way out, Cash wil stop you because of the new tank the militia has deployed. Exit the QCPD on foot and stalk the Cobra drone up close to find a weakness. Once examined, call in the Batmobile and engage the tank. You have to target the exhaust port behind the main turret. Get out of the tank's range and call in the Batmobile. Sneak behind the tank and destroy its rear exhaust to instantly destroy it.
After destroying the Cobra, you have to head to the clocktower facility to get the Batmobile's second upgrade. Follow the marked location and park the Batmobile on the hidden garage to receive the upgrade. Once done, bring Ivy to the Botanical Gardens in Miagani Islands.
You'll encounter three more Cobra tanks on your way. You have to sneak on them and destroy them all before you can continue. Use the Radar on the lower right hand corner of your screen to know their heading and location. Just sneak on them and when you get detected, use your speed to leave their range.
Once cleared, continue forth to the Botanical Gardens. After the scene, your mission list will be updated, including a new one. (Two-Faced Bandit)
When you're ready to continue with the main story, head to the parking garage of Wayne Tower. Park the Batmobile on the marked spot but you'll have to deal with the drones that breached the area first. After destroying all drones, park on the spot to get the Batmobile's Sonar upgrade. An army of drones will be deployed in the area again.
Use the Sonar pulse to track down the Ancient Root system. Take out the enemy drones as you make your way towards the center of the roots. When you find the center of the root, press and hold your Sonar pulse to wake up the plant. The militia will send a unit to shoot the plant. You have to deal with them to protect the plant. Fortunately, none of them are armed though they have a specialist that can give their allies temporary electric charges outside their armor. Use the Batclaw to short these charges. After eliminating all the guards, the objective will be complete and new intel about your ongoing missions will be available.