It is possible in 23 or less turns. I was testing out the walkthrough here (mainly the expansion bit as you need to get big fast and i was not expanding optimal enough for insane) with saved games so i could follow the walkthrough pretty closely. After the initial expansion similar to that of the walkthrough, I stoppped reloading and finished in 23. I wasn't pushing for maximal speed at first, but ended up attacking on 4 fronts and crushing big stacks on the other 2 fronts with abandons. This allowed me to go deep fast and secure a win in 23. It still was not optimal play as i made some mistakes and could have opened a 5th front just before playing an abandon.
I believe 22 and perhaps even lower is very possible if after the initial expansion, you keep pushing deep on multiple fronts while taking the 1's behind your big stacks and leaving their passed stacks for later in the game.