If an RPG can do it
I have seen a demonstration of a T-80 shooting down a low flying drone with a Reflex ATGM. It is just a matter of keeping the laser designator on target.
Hitting a helicopter overflying an urban area at low altitude doesn't take much skill, and neither is hitting a Chinook at an LZ
Reflex is an ATGM. It takes 16 seconds for it to reach a target at 5000m, but can't cope with anything flying over 300km/h. Russians see it as LOW utility round, and during Soviet era issues only about 3 (more likely 1) per tank. The intended use is for SNIPING from overwatch (my opinion). However they did follow up the Shilka with the Tunguska
Shooting a moving target from a tank gun is not much different from what infantry do, however the problem as I see it is not FCS (acquisition; and is there a search radar?!) but ability to track with the turret traversing.
Proximity fuse (shotgun round) is the answer since the infantryman depends on volume of fire also, and a tank can't do that. Even the old flechette warhead will do!
However elsewhere I pointed out that outside of the stony desert the average LOS for a tank is limited to maybe 2,500 metres, and more likely 6-900m. If helicopters are added into the range of targets for a tank, the threat area assumes a very large envelope! it seems to me the optics in most Western tanks will not allow this unless the crew are on overwatch, and helicopter overwatch at that! Helicopter overwatch requires viewing the parts of visible terrain which are NOT likely to generate ground targets! It seems tanks are still the 'killers' for ground targets, but accompanying IFVs (in current weapon configuration) are not able to engage helos at the 2,500+ range.
This comes back to dedicated AD assets vs 'hybriding' the largest part of AFV vehicle fleets (the IFVs/APCs) to cope with a variety of targets. It seems the warhead designers (tank or ATGW) are a but 'fixated' on the WW2 ideal of penetration
Then there is acquisition issue. Most current generation attack helos have mast mounted acquisition systems. This allows detection of ground targets from 'fuselage-down' hovers. Finding a tank is not so hard considering the mess they make when firing, never mind moving (apparently Mi-28Ns have directional acoustic sensors). This allows missile launch without initial detection. Even when warning does go on in the tank (for laser or IR seekers) the crew has literally seconds to do something!
Are you suggesting that the commander will elect to stuff around with FCS trying to acquire the attacking helicopter?! Hmmm...what are tanker balls rated in RHa?!!