Boxing is one of the best fighting style available, with a concentration on punches, head movement, footwork, and athleticism. So if you’re going up against a boxer, you need to nullify all of that! Grappling and kicks are a boxer’s worst enemy.
Chances are he doesn’t know much grappling so you need to break the distance, clinch and try to submit him standing with some standing chokes such as a guillotine, or a standing kimura lock. If there are no other potential attackers around, you can take the fight to the ground and use your grappling.
In this video, with a beautiful beach in Santorini as the backdrop, self defense expert Nick Drossos goes over some tips on how to defend yourself against a trained boxer.
A perfect example is Randy Couture vs Jmaes Tony:
Another great example of this is Royce Gracie vs Art Jimmerson in UFC 1:
Sloth Jiu-Jitsu: you can be slow and unathletic and still kick butt in Jiu-Jitsu.