I have recently reduced my working week to two days, its been suggested to me that I should sign for the other days to keep up my tax credits, can anyone advise me please.
I presume that you mean to sign on for Jobseeker's Benefit/Allowance? You can only do that if you're available for work on the days you're not currently employed.
If you meet the criteria for Jobseeker's, you will maintain your PRSI record (not tax credits).
Have a look at www.welfare.ie for information on claiming jobseeker's payments.