There are two important points to consider regarding your redundancy payment.
Firstly, if you are under 55 and get a redundancy payment of more than €50,000 you will be disqualified from claiming Job seekers Benefit for a specific period. This link for Citizens Advice identifies the period of disqualification. 
Secondly, statutory redundancy payments are exempt from tax. The statutory redundancy payment (the minimum your employer can give you) is a payment based on your pay and term of service. All eligible employees over the age of 16 are entitled to two weeks’ pay for every year of service and one further week’s pay. You must have been working continuously for your employer for at least two years to be eligible for statutory redundancy. The statutory redundancy payment is subject to a maximum earnings limit of €600 per week (€31,200 per year). Pay refers to your current normal weekly pay, including average regular overtime and benefits-in-kind – but before tax and PRSI deductions. That is your gross pay. As I said the statutory redundancy is tax-free.
To calculate how much statutory redundancy you are entitled to, you can use this calculator.
If you are receiving a larger sum, in excess of the statutory redundancy amount, it is likely to become taxable. You do however, have the option of treating it as income in the year you receive it and pay tax on this or else claim top slicing relief. Alternatively it is possible to reduce your tax bill on a redundancy lump sum by using it to make an additional voluntary contribution to a pension scheme. Your employer is obliged to deduct tax from all your income. They may take account of the basic exemption, that is the €10,160 plus €765 for each year of service. Revenue may inform the employer about the correct amount to be treated as tax free and the rate of tax to be applied to the rest. If this does not happen or if it is incorrect and you have paid too much tax, you should contact your regional Revenue office or engage an accountant to do this for you. It is important that you declare that you have received such a lump sum on your annual return of income to Revenue.
It is worth seeking professional advice here to ensure you reduce your taxes on redundancy payments where possible. To arrange a consultation to discuss this further email caroline@charlespcrowley.com