The description for it is very confusing. And it was very hard to do it for me. Just switching from just tapping Y to holding and going back was hard enough. Here's how you can do it easily (once you can do normal blade dodges easily): Do a normal blade dodge, but after each swing, let go of Y for a split second, and quickly press it again. I found that it doesn't matter how long you let go. If you just release it between each swing and are holding it when he's swinging, you'll do the takedown. However, if you're playing as (fully upgraded) Batman, it might not make sense to do this, since it would just be easier to jump over him, get a combo going and break the sword. However, for Catwoman, Robin, and Nightwing (and Batman w/o disarm, but with blade dodge takedown), it should be very helpful. But, ALWAYS DO THIS FOR *spoilers* ASSASSINS. They can't be separated from their sword. But also remember that they have a fourth swing and are generally faster.
I've only done it twice so far since I unlocked it, its quite weird. Sometimes it works for me, othertimes even when I press Y batman doesn't move away and I get hit with the knife, and then I get annoyed and just do the 'Beat down' move(Which works quite well, and if you just want them out of the way, you can just triple-stun them).
Its satisfying when you do do the move right though.
Pretty sure the description tells you that, while pushing the control stick away from your enemy, you're supposed to hold Y until you dodge the enemy's attack, release it and immediately hold it again until the next strike. Repeat 3-5 times, depending on enemy.
However, another way to say "faithful" is to say "clingy baggage". She is what they call a "land mine".