This type of compensation is known as Criminal Injuries Compensation, and it is designed to be an available source of funds for people who haven’t been able to secure a compensation settlement through other means.
Assuming you’ve already tried and failed to seek a compensation settlement, you only have two years from the date of the crime in which to bring the claim, and the incident must have been reported to the Police within a reasonable amount of time after the incident.
To reiterate, the Criminal Injuries Compensation Authority only provides criminal injuries compensation as a last resort. You will first need to see whether there are other ways in which you can be compensated: for example, by making a claim against whoever attacked you or by claiming under an insurance policy.
If you have any doubts then an initial enquiry to a solicitor will help you decide what your best option is.
If you are still suffering (emotionally or physically) as a result of a violent crime, then please consider contacting the Victim Support service, as they are a free service who have much experience in helping people deal with violent crime.