PhD Advisor not responding to emails for letters of recommendation
You may try to either visit him during his office hours (more or less Krebto's suggestion) or you might contact someone at the department who is in close contact with your advisor. The latter worked for me a few years ago when I had to get in touch with someone who simply ignored my (and other students') e-mails. After a few weeks, I asked a colleague of his to remind that person to respond to my message. That middleman should be a friend of both, yours and the advisor.
However, as you have been sending him messages for a year already, it looks like your advisor simply does not want to write that letter. If you keep pressuring him, e.g. directly in person or through a colleague, you might eventually get that document. But its wording might not be as nice as you had expected in the first place.
Maybe, you could also ask nicely, if there are any issues that the advisor wants to clarify before sending that letter. Those might be some details regarding your research.