If you have ever lived/worked in the UK for more than 6 months (im not 100% sure on that so someone may want to correct me on this) then you will need to get a disclosure Scotland otherwise you wont as they wont have any information on you so it will be pointless. AS far as Im aware the DAA require a 10 year background check on you for their security purposes, they seem to be much stricter than other airport authorities. Instead of a Disclosure Scotland you will need to get Garda vetting which is pretty easy to get and Im sure Monarch will help you out with this. Also you will probably need to get vetting from any country which you have lived/worked in for more than 6 months(again I may be wrong on the length of time).
The ID department at Dublin Airport can be a bit of a nightmare at times especially when working for an English company based there as the rules in England are different to the rules here but once you have all your references well sorted then it shouldnt be too much of a problem.
Best of luck and I hope you love the job!! Iv heard Monarch in Dublin are a great group to work for as its quite a small amount of crew there so its almost like a little family!!!