A fair few months late (apologies Dennoman!) here's an alternative method from Dennoman, which appears to be a bit more than twice as quick as mine. I haven't been able to test it as i've not owned the game in some time, but anyway:
"This solution courtesy of my pal FL Trooper BE.
Go to Versus with 2 controllers, pick Yoshimitsu, any partner, 75% handicap. Opponent should be Akuma at 100% health, as he has the lowest health in the Xbox 360 version of the game at 850.
Just spam Swordpoke Windmill (63214 + any punch). It takes 7 to completely fill up your meter. After the 7th, simply activate Cross Art. Akuma should only have the tiniest sliver of health left after the 7th and last Swordpoke Windmill, so the first hit of the Cross Art K.O.'s him. This shaves A LOT of time off your total spent to grind this, should be able to get an average of roughly 3 wins per minute, maybe 150-160 an hour.
Also, default or no gems equipped for both your and the enemy team. Nothing should be triggered during this. And make that a realistic number of 150-160 an hour if you're doing it very efficiently."
And a tweak by Infilament:
With a tweak to Dennoman's solution, I was able to consistently finish the round at 90 seconds on the clock.
Pick Ryu as the partner. Equip Yoshimitsu with gem 208 (4 special moves = 40% meter build) and gem 305 (4 special moves = 40% meter build, 10% damage boost, requires 2 slots). I think 305 is a special edition gem, but I had it. Then, you only have to do 5 swordpoke windmills with Yoshimitsu, followed by cr.MP canceled into cross assault, then do immediate fierce DP with Ryu. Yoshimitsu should also do some attack immediately, and you should kill Akuma. Should be regularly 89-90 seconds left on the clock!
If you don't have the special edition gem, you can equip the 3 special moves = 20% meter boost gem instead, and tinker with the formula a bit. There may even be amazing DLC meter building gems available in the future that work even better. But I do believe using Yoshimitsu's windmill move coupled with meter building gems is the fastest way to get the cross assault/cross art achievements. Using this strategy, you should be able to go from 0 activations to 500 activations/finishes in a little over 2 hours.
Here's the quickest method I found.
With Ken, equip the following gems:
#207 Onslaught lv.1 - Connect with 3 special moves
#212 Onslaught lv.2 - Connect with 1 launcher
#214 Onslaught lv.2 - Your partner connects with 1 launcher
Set up a versus game, best of 7 rounds, unlimited time (just incase you get sidetracked by watching tv, because this is really boring to do whilst not having a distraction).
Your team should be Ken first, and Ryu second. Set their hp to anywhere under 100% so the rounds don't get registered as perfect wins also. The opposing team should be Hugo first, and whoever you want second as they're irrelevant. Make sure Hugo has no defence gems equipped otherwise that might cock things up a bit. ALSO, MAKE SURE YOUR HP IS SET TO 75% SO YOU DON'T GET PERFECT VICTORIES. THIS IS IMPORTANT.
Anyway, at the start of the fight jump to Hugo, hit him with a launcher, and before he hits the ground, hit him with another launcher to bring Ken back in. That's 2 "Cross Gauge Acquisition Rate + 40%" gems activated immediately. Now start spamming Hadoukens until your cross gauge is full.
Hugo should be down to about 15% hp at this point. Activate Cross Assault. The beauty of this part (which saves a few seconds each round) is that from the full screen distance, 9 times out of 10, Ken will throw an EX Hadouken or a Hadouken. If you do the same, then Hugo dies most of the time. However, if you've done every hadouken perfectly in the build up, he will have a little bit of hp left so you'll have to throw a 2nd one. That said, you don't have to worry about moving across the screen to land anything, you can just do it while watching tv and not paying too much attention.
When I did this I could get about 20 wins an hour, maybe a few more, which is 80 Cross Assault finishes an hour approximately. So to get the achievement you're looking at roughly 3.5/4 hours grinding. ALSO DID I SAY, MAKE SURE YOU SET YOUR HP BEFORE YOU SET UP THE FIGHT TO 75% SO YOU DON'T GET PERFECT VICTORIES.
Please leave feedback if you have anything to add or have found a better method. A thumbs up would be appreciated, and if you leave a thumbs down please leave a comment as to why. Thanks. If you want to thumbs me down because you kept getting perfect victories then you didn't notice that I said MAKE SURE YOU SET YOUR HP TO 75% SO YOU DON'T GET PERFECT VICTORIES.