The T-Rex can be found by cleaning up the second area 'Carnivore Cove'. Once it appears you need to gain its trust by feeding it 5 King Ribs from the plants nearby. After feeding and harvesting the coins Newton will tell you that he had plans for a dinosaur saddle but they are on his broadband server which is locked due to another debt. After paying off the debt the saddle will then be made instantly in his lab. You are now able to ride the T-Rex by pressing
when facing it.
To get the achievement simply roar by pressing
at the amber crystals blocking the way beside the recycle machines.