Let's look at Portsmouth South in May 2010
Liberal Democrats 45.9%
Now let's fast forward to an AV election in 2015. Imagine that the Tories are moderately popular, they got they are up to 35% support. Meanwhile a third of Lib Dem support has deserted to Labour, bringing Lib Dems down to 30% and Labour up to 29%. That might be typical of a string of southern seats.
Now imagine that you're a Tory voter who wants to elect a Tory MP. It might increase the chance of a Tory getting elected if that Tory votes Labour. How's that? We'd assume that Labour 2nd preferences would tend to flow to the Lib Dems, the remaining Lib Dems 2nd preferences would flow towards the Tories (because a lot of the Lib Dems who preferred Labour would now vote Labour). So if the Lib Dems get eliminated then the Tory is likely to win, a Labour elimination would lead to a Lib Dem victory.
How can any AV supporter think that AV will end tactical voting? It'll just get rid of one kind of understandable tactics (if you don't think your 1st choice will win, you can vote for someone you wouldn't mind winning) with this kind of cerebral gymnastics.