Animals Act suggests that Animal OWNER has a liability. There is no LEGAL REQUIREMENT for you to have a gate. Also, it should not matter whether the farmer is insured or not. If he is liable, then he must pay. If he is insured, so much the better as then the insurer will pay. In the current economic climate, you are probably better with an insurer as the chances are, that the insurer has enough money to fix your garden.
On your side, you must remember that you can only claim for what puts you back in the pre trespass position. If you had a rough grass plot at the time of the trespass, then you cannot expect to have a newly rotovated lush lawn afterwards. You cannot expect the errant farmer or his insurers to give you a better lawn than you iniitally had.
Also you need to remember, in the interest of community relationships, that you are both neighbours and someday, perhaps in the distant future, you may need the farmers help and assistance. Don't ride him for the sake of a few euro!!!