IMHO, effective training would involve skill training (so, lots of doing the same thing over and over, like climbing, shooting, escaping handcuffs, etc.), physical conditioning, and putting it all together in simulations. This could take a lot more than a year to do properly - vo-tech training takes about two years for a number of rather mundane jobs where you are neither risking your life, nor trying to outsmart another person who probably doesn't really want to be assassinated.
As I see it, the way to make it fun would be to go with an apprenticeship type of education, where the trainee has to pay for her education by working for her master. The actual training will happen between runs, and the runs will be the work she does as payment - but they'll also show her how much she's improving. She'll likely be started off doing support work like researching targets and casing joints. As she gets better, she might be sent to do negotiations with Mr. Johnsons (nothing says, "my time is valuable" like sending a flunky to do the talking for you), to bribe people who the master needs to look away, or to steal useful pieces of equipment (they can't track your purchases if you didn't buy it!). Eventually, he'll start sending her on low level assassinations - kill the factory worker who beats his wife, shoot the bottom-level ganger who's latest victim wants his revenge before he leaves the hospital, stab a minor drug dealer who's providing unwanted competition, make the corp wageslave's death look like an accident because his boss will get a negative performance review if he fires any more people, etc. They'll get gradually more important as she moves up from thuggery to murdering the wealthy, the powerful, and their enemies. Eventually, she'll get the big job that serves at step 4.
I'd avoid ever having her accompany her master on a run (although maybe watching through VR could be part of the training bits you skim over). It isn't usually fun to play sidekick to an overpowered NPC. Besides, realistically, if a master assassin is carrying out the big hit of his career, does he really want to have his naive student along with him?