Hi Sam
Have a look at our PIP MR & Appeal guide for details of the process, the PIP area also has template letters that you can use to make the request with. It is half way down the page under 'Appeals'.
www.benefitsandwork.co.uk/help-for-claimants/pip You should contact the DWP for a copy of the assessment report if you have not already done so, I would phone them but again follow up the request in writing. Once you have the assessment report you will have a better understanding of how the DWP Decision Maker has come to their conclusions and will then be able to argue against them.
Your primary task is to show that you meet the criteria, there are many reasons you may have failed, you need to address each of these but don't get bogged down in criticising the assessment report unless you can clearly show that it is incorrect, it is a lot easier to argue the facts of the situation.
Gary