I would follow up the letter with a phone call or visit to the property to confirm a) that the tenant received the letter and b) that he/she understands that you will be obliged to take action should there be any further complaints.
I would also ask the 2 complainants to put their complaints to you in writing detailing the nature of the complaints, the times and dates of the incidents and any other relevant information they can give you. Also ask them if they would be prepared to act as witnesses if there should be a case taken with the PRTB. If they're not prepared to do this, they have to understand that it makes it extremely difficult for you to take any action against the tenant.
In return, I would mail a copy of the letter you sent to the tenant to the 2 complainants to show them that you have in fact taken action.
As your tenant has a fixed term lease, you will have to prove that he/she or others residing at the property are guilty of anti-social behaviour. You therefore need to make sure you have all the relevant paperwork i.e. Garda report, council complaint copy, letters from 2 neighbours detailing their complaints, copy of your letter to the tenant and a time log of all complaints, who the complainants were and your reaction to them. If you can get photos or video footage, that's even better.
If the tenant at any time fails to pay the rent on the specified date, you should immediately issue a
Rent Arrears Notice and, if the outstanding rent or any part thereof is not paid within 14 days, immediately issue a
Notice of Termination of Tenancy. Read the instructions of how to word and serve the notices carefully, if they are not served exactly as laid out, they will be deemed invalid.
I had the same issue with awful tenants last year who were dealing drugs from my property and attracting large numbers of teenagers to the house, which is in a very quiet cul-de-sac. These teenagers damaged my neighbours garden walls, they literally kicked them in, and threatened to damage cars and all sorts. However, I was unable to go after the tenant for anti-social behaviour as the neighbours were afraid of him and wouldn't complain to the Gardai or put their concerns in writing to me.
In the end, I had to use the rent arrears notice and the Gardai to get them out. They did around €2,000 worth of damage to the property and we also had to pay to have the neighbours walls rebuilt.