So this is the way I like to approach accent training. There's a three-pronged approach.
The first is to look at the aural posture of the accent that you're trying to emulate. And the aural posture is simply just where native speakers hold their lips, where they hold their tongue, is it in the front of the mouth, in the back of the mouth, how fluid is the jaw? Does the jaw move a lot, or does it move very little? These are all things that you can find out by studying with your eyes native speakers. So look at native speakers talking and see where they're moving their articulators.
The second thing I look for are the sound changes, so what are the specific sound changes of that accent? So do they do their ths "th" or do they do them "th, th, th." And you want to drill those sound changes so that they become second nature to you.
And the third thing I look for is kind of like the magic bullet of accent training, and that's musicality. How does the person express themselves? Do they use volume to emphasize words or do they use pitch? Is it an urban sound or is it a more rural sound? You can look at the climate of a specific area and that will affect the musicality of an accent.
So the three ways we'll look at accents are through aural posture, sound changes, and musicality.