TL/DR: there are other aspects of talking/hearing besides pure accent. Learn to ask some questions that make it easier for you to understand.
I (sometimes) have this issue with no other than my wife! We are both native Spanish speakers and in my country there are no big accent diferencies from one region to another. That's why I want to add tho the current answers by stating that there are other issues besides accent that can hamper communication.
In our case there are mainly two aspects:
- In my country there is a kind of "sluggish" way of talking that we normally use with people we have confidence with (family, close friends, every day-contact colleagues) that is characterized by the very few words of every phrase being rushed or "squished" together and pronounced softly, somewhat muted. The ending of phrases is more well pronounced and we normally fill up the missing words by understanding the middle and last words of the sentence, but shorter phrases get challenging. By contrast, a person speaking on the phone, speaking on a meeting, etc, still has the local accent but usually "speaks up", initiating phrases with normal loudness and not rushing or squishing first words.
I categorize this effect outside "accent" because it is situation dependent.
Please observe if your issue with your boss persists when she/he is speaking to a group, on a meeting or if you happen to be there when she makes or receives a phone call. If you notice a difference, then there might be something like this, besides pure "accent" going on.
- Context. When the conversations have been going for a few minutes, there is no big problem, but at first, when the one not initiating the topic hasn't completely switched their attention towards the new subject, it becomes a bit frustrating because we have to "wait" for the other one to "catch up". After a while, the brain kind of fills in the hearing gaps by virtue of "knowing what we're talking about". This is kind of the same thing as when you are reading a familiar subject and your eyes just glance over some of the words and you don't actually read each an every word but rather assume that some word "goes there". (I think) the same happens to hearing. By contrast, when reading about an unfamiliar subject, one usually reads slower and paying close attention to every word.
In a work environment, I've observed that the boss may come up with a new subject after having a meeting with their superior or other department bosses, and so, their mind comes loaded with a lot of details, like the base objective for a new project, the issue to solve with a new methodology, etc. So when he/she speaks to us, it's common for they to jump to the middle or end of the story, and speaking fast due to excitement. But for the rest of us, the brain gets busy trying to tie up a bunch of ideas and solve the puzzle of what's being said, and while that happens, hearing power "decreases" (you no longer have free, "idling" brain power to work on filling in the blanks left by speaking/listening/ambient noise problems.
In my workplace, this issue has been detected and our boss now begins team meeting by explicitly citing context (he even says the word "Context!") and while he explains the base issues or purposes of what comes next, he actually causes everyone to "bring to (top of) mind" a bunch of related information (we are software developers, so this information is recalling where this particular data is stored, what user interfaces are involved, platforms, etc). Once we have all this context in mind, it becomes much easier to understand the general picture, which is very often expressed in a very fast pace, due to either "too much enthusiasm" or the job being "very urgent".
On a separate anecdote, I've had a friend ho speaks really fast ant tries to give too much details. In that case, since he's a friend, many of us who know him, have told in polite ways that he speaks too fast (particularly the the topic is exciting to him) so now he is used to being told to slow down. He even does it by himself we he gets our "lost in a forest" stare.
So, to summarize and try to answer: Learn to make questions about context and clarification, some other than "please repeat". Ask context questions at relevant intervals to consciously slow down the conversation, ask for conclusions and repeat to her the main points with your own wording to make sure you understood.
Use your voice tone to regulate the conversation pace, somewhat like speaking calmly to an irritated person is more effective than actually saying "please, calm down" (I've had some success by speaking "like a news anchor").