Here's the strategy I used.
Knock out 4 of the 5 arms (or however many there are, just be sure that there's only one remaining). The one remaining can still move around, but only on one side. Stay on the other side so it can't get to you. If you eliminate all of them, they'll come back, so it's better this way.
As for the actual Leechgrave, draw an imaginary line around it using its four "arms" (the tentacles that stem off of that bulb). Inside this perimeter is where it can melee you (with the ghost arms that pop out of the coffin.
So here's what you do. Go just inside the perimeter and wait for it to do the melee. As soon as it prepares to do so (the grave should swing back and creak open), dodge roll out of the perimeter. Then, after the attack, air dash back in and combo the grave.
How much you can hit it depends on what Keyblade you're using. Mine had short 3 hit combos, so I could just fit in 2 combos max. Anymore and it will hit you with the melee.
After you experiment and find the right number of combos, be sure to use that amount of hits each time. And when you do, quickly dodge roll several times out of the perimeter. If the grave hasn't tried to hit you already, nudge back into the perimeter and wait for it to prepare to attack (doing the same as before).
The key here is getting it to attack you, dodge rolling away, air dashing back, comboing the right amount, dodge rolling out, and repeat.
It may not always try to attack you right away. Or it may use the rapid firing purple spores (you can tell if the grave turns backwards), which can be easily blocked.
Also be wary of the poisonous mist that shoots out of the bulb around the perimeter. When the mist is coming down, don't bother with attacking. Get out of there and wait for the mist to dissipate.
It's a highly tedious strategy, but it definitely works.
The first time I fought the Leechgrave, I worked out most of this technique by staying back, experimenting on the tentacles, inching my way in, and noting its attacks. Except, instead of dodge rolling out of the perimeter, I tried blocking the grave's melee attacks. Not a good idea. It does work, don't get me wrong, just not all of the time. Occasionally the ghost hand (being very erratic), will manage to hit you (from the sides or even the back) despite your block. I wouldn't recommend it.
