So, after many hours of trying to get this trophy (it is by far the most difficult trophy in Sly Cooper history), I finally succeeded (and it is, in fact, a double platinum if you own both the PS3 and Vita versions of the game)...
Japan Arcade: Alter Ego (Jetpack Bentley hack). Score to beat: 25,000 (easier on the PS3 version).
Collect every ionic bit you can to get to Level 10 as quickly as you can and do your best to stay there (be sure to hit the portal in the middle of the first phase for free points/ionic bits and a Sly Mask). Shoot everything that moves, and you should have somewhere around 22,000 points (or better) when you reach the CPU boss. To get the high score (25,001+, hover behind one of the blocks so the CPU can't hit you, and continue to shoot the blue blobby eyeball that the CPU spawns pretty regularly, taking care not to kill the CPU too quickly, because that ends the game. Once you get your score over 25,001, feel free to either die or kill the CPU to end the game.
My Best: 25,327
Old West Arcade: System Cracker (Tank hack). Score to beat: 4,500 (easier on the PS3 version).
Pretty straight forward here. Just kill everything that moves. When alternate tanks are available, you can switch tanks when you are running low on health (each tank has its own health bar), and switch back when needed. Health drops are very few and far between, so you will need to take great care at avoiding getting shot or colliding with enemy vehicles. The green tank's health does not regenerate between levels. You should have the high score by the end of level 4. With the purple tank on the second level, blow up the wall on the right side for a Sly Mask.
My best: 4,562
Ice Age Arcade: Spark Runner (six-axis hack). Score to beat: 1,000 (easier on the Vita version).
Simply pick up the purple timer upgrades around the start point and the upgrades to the left, then roll between the bumpers beneath the start point and allow your spark to bounce between them until you run out of time. If you have 20 seconds or more when you start bouncing between the bumpers, you should easily beat the high score. After you hit bumpers a few times, a Sly Mask will appear in the upper left corner of the maze.
My best: 1,290
Medievel England Arcade: Super Alter Ego (Jetpack Bentley hack). Score to beat: 20,000 (easier on the PS3 version).
Strategy for the high score is the same as the Japan Arcade. Level 10 as quick as you can, stay there, hit the blue blobby eye thing until you reach the high score. Sly Mask portal is in the middle of the second phase at the bottom of the screen as the level starts moving upwards.
My best: 20,144
Arabia Arcade: System Cracker Extreme (tank hack). Score to beat: 4,500 (easier on the PS3 version).
Strategy is the same as the Old West arcade. This time around, though, you'll only have access to one tank at a time, but the game is a lot more generous with the health drops. You should reach the high score at some point while you are using the Blue tank. The Sly Mask can be found on the sixth level (Green tank for 3 levels, Purple tank for 3 levels) to the left of where you spawn (behind a destructible wall).
My best: 4,737
Paris Arcade: Maximum Chaos (mixture of hacks). Score to beat: 4,000 (easier on the Vita version).
First up, Alter Ego. Just get through this portion, as you won't really have a chance to score a lot of points (and there is no blue blobby eye thing during the CPU boss fight). The level moves much quicker than it has up to this point. You'll likely end this phase with around 1,500 points or less.
Second phase is Spark Runner. This is where you are going to earn your points (and a gold trophy... or two if you have collected all the Sly masks elsewhere in the game). Simply go through the level normally, collecing all of the timer upgrades you can. If you start to run out of time or start to fall of of the board, quickly hit the start button and restart checkpoint (you will NOT lose the score you have to that point, but you will restart at the beginning of the Spark Runner phase). Repeat until you exceed the high score. The Sly Mask can be found at the end of the Spark Runner level at the top left of the board on the same platform as the finish.
My best: 5,693.