This is one of the most annoying trophies in the game, not because it's hard to win with heavy engine damage, but because it's hard to get heavy engine damage in the first place without destroying the rest of your car.

The strategy will be to do several stages in a row in which you damage your car, and between the stages, you will repair your non-engine parts but not repair the engine. Eventually, the engine will have heavy damage while the rest of the car is still functional. Then, in the following stage, you can go for the win.

From the main menu, go to Quick Play > Solo > Create Rally. Under Championship Settings, set the AI difficulty level to 1 and turn on hardcore damage. Then go to Create Championship > Add Event and select a car class of your choice. Choose Rally Portugal and add a lot of short stages, which can be the same one multiple times. One good option is route #11. Feel free to add 8 or more copies of it to make sure that you have enough stages available. You won't actually have to complete all of them. Change the Service Area setting to Long for each stage so that you can do repairs to the non-engine parts. Then, choose Confirm Event > Confirm Championship > Start Championship and select a car of your choice.

Start the first stage and crash into trees or other heavy obstacles a few times to damage your car. Make sure that you don't go too fast though because otherwise your car can be totaled in a single hit. If this happens, you can restart the stage. After you feel that you did some amount of damage (the radiator light should be on) you can finish the stage.

In the Service Area, go to Vehicle Setup > Repairs and check how strongly the engine is damaged. After one stage, it probably won't have heavy damage yet. Use your available time to repair other parts of the car that are damaged. Then start the next stage.

Now repeat this process until the engine shows heavy damage on the repair screen. Then you can go for the win on the following stage, which will unlock the trophy and shouldn't be too difficult to achieve against opponents at AI difficulty 1.