It seems every 10th thread in the North America section is about getting a FAA certificate.
1. You need to have your CAA validate your license to the FAA. (This allows you to skip the FAA private and commercial certificates.)
2. You need to pass a TSA background check.
3. Complete a ATP certificate training program.
4. Pass the ATP written.
5. Pass at least a 3rd class FAA medical.
6. Pass the ATP checkride.
If you are going for a type rating in a sim you do not need a medical but you must have a record of ground and flight training and an instructor's signoff for the checkride.