I must be missing something here . There's nothing comparable under the medeival line up to demi gods . Being a rookie, what's the best way to waste these buggers ?

Have you tried massed ballistas with attack strength fully upgraded to Expert Weapons and a commandeer within 3? Fire from within a barracks for extra punch (but not if enemy has catapults in range).

Demi's I'd guess are extremely expensive which means there will be less of an army to back them, ranged to pick off anything in the way and reign in on them while they are pummeled by melee, a good number of scouts is always nice fodder with knights doing final blows might work, or u could go pure basic again it which would probably work well. Arbalisters are a great choice for ranged especially since they do well in melee for when that demi jumps ur zoc.

I haven't played in a while, so I won't comment on too many specifics, but the key thing you have to remember is they only get one attack per turn. The worst thing you can do is go after it with just a few valuable stacks, as that's exactly what the other player wants. They will be trying to get max value from their demi, which means doing the most damage each turn, i.e hitting valuable troops for full damage every turn: attacks against lesser units severely decrease the demi's usefulness (and non-attacking turns are points/gold wasted). If all he can do is attack spearmen, for example, then he's no more powerful than any other unit that can 1 hit that unit.

That said, demis lvl up easily (with high damage, hp, and flying type), so feeding them lots of weak stacks will backfire in the long run. Thus, a balance is needed. Strong units are necessary to do any significant damage, but weaker units are just as necessary in protecting those units from powerful counter attacks. If the demi also has supporting units (and he almost always will), then the question becomes chip away at the demi or take out his defenses first?

The answer is tactical, and thus dependent upon individual situations. The general rule is that your attacks should remove your opponent's ability to deal damage, and your subsequent defense should maximize protection of your own damage dealing units. The demi does a huge amount of damage, but it is very situational damage: if he doesn't attack, or is forced to attack weaker units, he is loosing quite a bit of damage value: thus, if you can keep the demi under control, it is usually more prudent to take out his support first (as they will be doing more damage). If his damage is, or will soon become a major factor (or the battle will take so long he'll be gaining many lvls off your weaker units before you get to him) it would be wise to coordinate a concentrated attack against him. It's a very tough call to make: it relies on you making the right calculations, with the right information, and being able to implement that decision with accurate tactics. In practice, the demi will usually not be the first target, but will rarely be the last.

As far as specifically downing him, ranged units are obviously key for the Medieval race: even enough archers will be able to wear a single stack down (and even kill him with enough stacks). One should be looking to maximize damage every turn you decide to attack the demi: with large hp stacks, the difference between killing 2 units and killing 3 can be huge. That said, if you kill 2 units, but know you won't be able to kill a third with what you have left, you're better off killing other enemy units (as this will actually diminish the enemy's counter attack). Melee units should be used sparingly, particularly valuable ones such as HC and Knights. If you don't do enough damage in your attack, the enemy's counter attack could very well take out an entire stack of these expensive units (remember, demi's like nothing better than hitting valuable stacks for massive damage). If you are confident you can do more damage than the enemy's counter attack will do to you, go for broke: otherwise you'll have to whittle down the demi gradually and protect your units from big hits.