DDT (Dark Dirigible Titan) Bloons are a MOAB (Massive Ornary Air Blimp) class balloon. These are the black bullet-blimp shaped enemies that are the fastest of the MOAB class balloons.
You will not find these until Round 90 (or 88 on Alternate Bloons game type variant).
BAD (Big Airship of Doom) MOAB balloons (the super slow but extremely strong Purple blimp boss balloon encountered first at round 100 as the end event boss) will also pop-down into 3 of these.
DDTs have Camo, Lead, and Black properties.
The main weakness these balloons have is to upgrades that target MOAB enemies specifically. For example, MOAB SHREDR and MOAB Mauler. So have towers such as Bomb Shooter (cannon-looking tower) and upgrade it to a result that has at least 0-3-0.
On levels with water, I like to have the Monkey Buccaneer and upgrade it to have at least 0-4-0 to activate Monkey Pirates. 0-5-0 is even better with Pirate Lord. Monkey Pirate gives you a user-activated ability to shoot a single hook that drags in a DDT (and several other types of MOABs). Pirate Lord upgrades that to 3 hooks that can take down all but the strongest two MOABs as single hit kills. This will also work you towards the 3000 hook kill in-game, but not Xbox, achievement called Hook, Line, and Sinker which unlocks 100 Monkey Cash, 0-4-0 Monkey Buccaneer, and 0-3-0 Druid.
You could tie this is in with the Hero Pat Fusty who learns the ability Big Squeeze at Level 10 which instant kills a DDT balloon.
Due to the DDT appearing only late in the game, you'll be wanting to play Hard levels in Single Player or Coop.
There is an in-game, but not Xbox, achievement for stripping the fortification off 3000 DDTs that you can incorporate into this that is called Crash of the Titans which earns you 300 Monkey Cash and 0-0-4 Mortar Monkey. Don't use the hooks if going fo that one as killing a DDT that's still fortified won't add to this in-game achievement.
This achievement will unlock naturally with play. It is not a fast achievement but there shouldnt be any reason to focus a grind specifically on this.