When thinking about defeating a tank, consider a tank is nothing more a then 3-6 (in our case 4) people in a armored shell rolling around. A tank without it crew is nothing but a very heavy (and expensive) barrier. Your objective then, can been always be thought as stopping the humans from controlling the vehicle. Either by death, immobilization, inability to project harm, losing the will to fight or incapacitation.
In short summary, the most effective organic threat to a tank already exists - The human and it's mind.
Creating a creature that has near or above human like intelligence, that is hard to see, even harder to hit and capable of ambushing or otherwise closing with a tank with some degree of speed and stealth. Then the tank is yours. A tank cannot engage at point blank and servery blind to anything in the near range.
To kill a tanks occupants with ease, you can attack though the weakest points. This being the optics or the neck of the turret. This could be done with some chemical attack much like modern HEAT weapons, a very high powered thrust of a piercing tip or with enough intelligence you could wait till they open the top hatch and destroy the occupants.
If there is some magic of biological evolution, creating a massive shockwave to the roof of the tank which can be done mechanically like the pistol shrimp. If the waves are directed and don't have a chance to disperse in air, the armour works against the occupants and translates the waves into the working area. Such a force would liquefy the small veins inside the occupants and render the occupants promptly dead.
About your prey
Tanks are primarily thought as mobile demolition platform (which supports infantry) or the modern equivalent of fast charging calvary/knights or mobile impervious forward facing, pillboxes, that provide flexible defense against everything.
These idea of roles, thus defines much of there power and limitations. Limitations that can be exploited to defeat Modern Armour like the M1A2.
As I write below draw from it, the ideas of explotiation. That's truly all that war is. Seizing opportunity and capitalizing on the weak points of whatever you are fighting. Play to your strengths and to their weaknesses. Don't fight a Tank for what it is - a brick wall. Fight it for what it is not - an anti-air or missile defeating platform, an all seeing close quarters killing machine, an fast moving, all terrain, mountain climbing, long range artillery piece.
In the case of the M1 Abrams. It was designed to defend against hordes of Russian tanks, and then roll and maneuver with great speed on the plains of east Europe towards Russian heart land. The tank sports a lot of features that helps it one up its prey and allow it out survive its cheaper and more crudely designed counter parts. A short list is that it can lower (depress) it main gun more, accelerate at great speed, shoot father ranges with more accuracy, better gun auto stabilization, better tracking of threats and exceptional optics/digitization to name a few.
Tanks and even historically all armoured fighting units, due to there exceptional armouring have always had to strike a balance between mobility, visibility and dexterity to achieve a high level of functional armour. Sacrificing movement speed for armour, destroying visibility in a enclosed hull, helmet or shield fort to provide the highest degree of protection from threats of all angles (Since the Romans), some removing the top turret and non forward facing armour to provide the most armour where it is needed.
The M1 overcame the mobility issue for its heavy tonnage by placing a jet engine within its body. The jet engine provides exceptional acceleration and mobility infers the following major penalties.
- Lights people and things on fire
- Loud with a unique sound signature.
- Huge fuel consumption
The American idea was that they wouldn't try to sneak the tank around a quiet battle field, stray far from infantry nor would they stray far refueling and logistics.
All, if by factors of war, become not true - puts the tank at a severe disadvantage.
In a tank vs tank scenario, unless your tank is offline - you wont be hearing the enemy tank from inside your tank. With the concept of a organic beast, it could produce no noise except for the impact of "feet" on the ground - which could be organically muffled. A tank like a M1A2 could be detected even idling at great distance to trained ears.
The heat produced from the tank is impossible to despise, even when idling. Any creature that can see heat, would be at an exceptional advantage against any metal armour - as it would heat in the sun, and be exceptionally hot if running.
Fuel is a problem for armour, if a battle is prolonged. For an inferior fighting force this might be an option for destroying the fighting ability of your enemy. Rather then blow its hard to kill (see WW2 German) tanks. Destroy the depots and the refuelers, and the battle will be won eventually by attrition. Do also note, the tank crew needs to eat, drink and poop. If the tank was immoblized, (by chemical entrapment, falling into a huge hole dug by your creature, pushing the tank of the cliff) a creature could just wait like a spider - until the crew is forced to try to flee. For all that matters, it could sleep on the roof to conserve energy :)
About your creature
In open face to face combat. See Rhino vs Tank. Your creature would require nothing more then a faster speed then the turret could traverse. Once it gets closer human powered machine guns would open up on it. However if it was armoured, that could be defended against. If was wasn't, it would have to dodge human manned fire in great volumes which would be difficult unless it was hard to track or see. Also the humans could be surpressed from ever exiting the vehicle, thus defeating the use of external guns.
Tanks are in no way as flexible or as agile as a human with a gun. They exceed in speed but not always mobility. Exploiting that is critical. This can be done though the use of ambush, stealth, ability to traverse different terrains or speed. A slow moving large target, would never survive against a tank. It just drive away and pummel it from whatever distance it could muster. Presuming the weapons are strong enough to hurt your creature.
Adding to this. If we keep with your idea of aggression (probability, all the time). We do not want to be some form of trap door spider or incredible horse sized tunnel worm that only works purely on ambush. So at this point your becoming limited to a fast moving or limited sized (horse) unit. Slow, large and ranged unit - isn't effective, unless it mimics the AT properties of a modren HEAT round.
If your creature was social you could look at the idea of a wolf. Because a tank is limited at shooting one thing at a time, and whatever it is trying to shoot at it - it has to hit it with a 7.62 to 120mm sized round. Again with the top surpressed, limited to one thing at a time (without CROWS). So in the wolf or really Bug/Zerg/Tyranid/Hord style combat scenario, the tank is quickly overrun even when faced with fighting the units head on and/or in ambush. The reload time of a M1A2 is about 5 seconds. If the unit(s) can close the gap after a miss or a single successful hit, it is again over for the tank.
The tank is also susceptible to prying motions, with enough strength the barrels, tracks and neck collar can be damaged with far less force then which is needed to punch though composite ceramic, steel and DU.
I hope this helps.