A client had passed on a huge amount of data that was collected as part of business operations over several years

A client had passed on a huge amount of data that was collected as part of business operations over several years. It contains several lists or tables with duplicate and unorganized data. There are big lists with unrelated information piled in a list format. The data, collected over several years has become unmanageable and full of errors (since there are duplicates) and is of no use. How would you go about "convincing" your client to "re-design" the database and normalize the tables for efficient usage.  

Support your choices with reasoning.

• ?? Write a professional, and complete explanation of your choices.
• Explain and discuss why the tables need to be normalized for data integrity and retrieving useful information