For time, you'd probably want to drop before the boss, play as the other character, gather enough DPs to purchase the Drop Decelerator level 3 bonus (I believe it's 200 DP). Alternatively, use at least one Drop-Me-Not before engaging the Clawbster (and other bosses in general) to refresh your drop gauge and drop rate.
As for tactics for Chill Clawbster, well... I know he's a flaming pain because he likes to fly up so high it's almost criminal, causing you to be unable to reach him. I'd say when he's grounded, use commands that can cover a huge distance to get to him such as Sliding / Thunder Dash, and then whack away. You might want to try the Icebreaker command if you already have one from KO Kabuto. It's essential that you dish as much damage as you possibly can before he flies away.
Also, try Balloon or Balloonra (or Balloonga if you have R&R Seal and have already unlocked it); they are essentially the Mines of DDD and are deceptively useful. Bear in mind though that Balloon and Balloonga only activate when in contact with the enemy, and while you can launch projectiles with Balloonra, they might not be fast enough to catch up with the Clawbster if he moves too quickly. They might also not be able to reach him when he's so high up, so I think your best bet is to pull off a Balloon or Balloonga underneath him when he's grounded for a decent damage output.
EDIT: Ninja'd by Master Spockanort, but I'm glad that it's not only me who's frustrated with Chill Clawbster. XD