I would recommend first upgrading to 2.9 (See guides here: https://book.cakephp.org/2.0/en/appendices.html) The reason is that a number of changes was done to help make the upgrade path a little bit easier.
Second is to upgrade to CakePHP 3 by following the guides here: https://book.cakephp.org/3.0/en/appendices/3-x-migration-guide.html
Unfortunately the 2.x to 3.x upgrade is a rather challenging one for a large application, but one that is definately rewarding. The upgrade tool does help automate a lot of the find/replace type changes, but due to the complexity of the changes (Especially with the ORM) it's not possible to automate everything.
Once you've run the upgrade tool it really is a case of working through error by error until it works.