There are currently 5 Burst modes:
-GigaSeadramon (Giga scale) Level 255
-TyrantKabuterimon (Tyrant Crow) Level 260
-ChaosDramon (Hyper Cannon) Level 245
-VictoryGreymon (Dramon Breaker) Level 250
-ZeedGarurumon (Zeed Cannon) Level 270
[kosnova did GigaSeadramon and TyrantKabuterimon]
[ohpaper did ChaosDramon and VictoryGreymon]
How to Get:
Go to Deadwood Castle off of the desert, then once your at the castle look on the wall to your left. You should see a Purchase Unlocker sign, as well as the needed requirements. However, to buy the Unlocker, you will need 10 Dark Spirals, 20 Virus Chips, 50 Black Gears, 75 Obsidan Chips, 3,000 Cash (you can sell Black Gears/Dark Spirals to get the cash),100 Red cubes. and finally 500 Ice Shards.
In the new 2017 update, you just need 10000 cash to buy one unlocker.
There are also three more Bursts:
Omnimon [one of the rarest bursts to get]