For the A, where it slides a quarter tone down and then up to a quarter tone high:
While lipping it down the quarter tone, slowly and smoothly (so that it is inaudible) press down your right hand (f, e, d). then, when you bring you embouchure back to reality, the pitch will be the quarter tone sharp, so you don't have to lip it up, cause that's a pain. Be ware though, you'll have to lip it further down, about a half step total, because lowering your right hand will raise the pitch significantly (which, after all, is the goal.)
Good luck!
While lipping it down the quarter tone, slowly and smoothly (so that it is inaudible) press down your right hand (f, e, d). then, when you bring you embouchure back to reality, the pitch will be the quarter tone sharp, so you don't have to lip it up, cause that's a pain. Be ware though, you'll have to lip it further down, about a half step total, because lowering your right hand will raise the pitch significantly (which, after all, is the goal.)
Good luck!