(Like Portal TFV, I had played this before Kongregate, but played through it again to get the badges. Yay badges!)
Indestruct2Tank (the somewhat peculiar internumbering is because this is a sequel to the original IndestructoTank, not currently on Kongregate) is a game with a thoroughly ridiculous, yet entirely enjoyable, premise.
So, here's the basic idea. You have a tank, which is indestructible, as the name might imply. A massive flotilla of airplanes and helicopters battles you by flying around and dropping bombs on you. The good news is, as mentioned earlier, that you're indestructible. So all the bombs do to you is cause you to fly up in the air. This is actually very good news, from your standpoint, since when you're up in the air, you can collide with the enemy airplanes and helicopters and destroy them. Each collision also gives you a little upwards boost, so you can rack up massive combos in which you destroy tens of enemy vehicles before touching the ground again. Large combos are far more profitable in terms of points than destroying vehicles one at a time, so there's a fair amount of skillful maneuvering required in order to keep aloft for as long as possible given the available enemies and their ordnance. The catch is, of course, that your tank isn't completely indestructible. (There's always a catch...) As time passes, your fuel decreases, and if you happen to run out of fuel, your tank (somewhat inexplicably) explodes. The only way to prevent this is by reaching some goal before running out of fuel.
So, like I said, completely ridiculous. (To ask the most obvious question, why don't they just, you know, stop shooting at you?) But pulling off a combo of 30 or 40 is extremely entertaining. There are two basic game modes: regular mode and adventure mode. In the regular mode, you have to accumulate a certain number of points to finish the level and refuel your tank. When you advance a level, you can spend the points you've gotten on increasing the frequency of enemies that attack you (which you'll need in order to get longer combos in order to get the higher number of points required to advance to higher levels). In adventure mode, you just have to survive the length of the level to advance; interspersed are various cutscenes which advance the (thoroughly ridiculous, appropriately enough) plot. There are also boss fights in which you have to defeat the boss before running out of fuel.
The one flaw in the gameplay is that sometimes enemies just won't show up when you need them. This is especially irritating in adventure mode, where some of the later levels are filled with obligatory bottomless pits, and sometimes you just end up falling into the pit because no airplane is considerate enough to fly by and bomb you in time. Conversely, sometimes the screen is just filled with so many enemies that you couldn't possibly get all of them, which only makes the preceding situation that much more frustrating.
The presentation is not bad. The programming itself is solid; there aren't any glitches or problems (at least that I could see), the graphics are fine if a little vanilla, and the sound effects are serviceable. The music is OK, but since there's only one track, you're going to get pretty tired of it after a while (which seems to be the case, really, for nearly every Flash game that lasts longer than a few minutes or so, so maybe I shouldn't be too harsh here). There's even some voice acting in the adventure mode, which is by no means great, but I definitely appreciate the effort.
Kongregate only awards two badges for this game, but there are a bunch more you can get within the game itself, which unlock some not-particularly-interesting rewards. So in conclusion, it's definitely a fun little game worth playing if you want to get the Kongregate badges. I enjoyed playing it to unlock everything, but that's mostly because I'm a horrible completionist.