Hm... This one is trickier to deal with, since there are so many more variables.
Let's see. At maximum setup, Legacy will be at +4 damage dealt, -2 damage taken, 2 damage dealt when Scholar plays a card, +2 hp when Scholar uses a power, and 2x1 damage Scholar deals himself each turn. Plus 1 one-shot each turn and his in-game effects.
Ingame effects:
Front side: 3 damage
Back side: 2 damage, -1 damage taken, heal 4
Oneshot effects:
1 damage, Scholar can't deal damage if he takes damage this way (x2)
2 damage (destroy equipment cards - irrelevant) (x3)
Discard a card (and chain to something else (x3)
3 damage, discard 3 cards (x2)
4 damage, destroy 2 ongoings (x3)
2 damage, destroy an ongoing or discard 2 cards (x2)
I'm going to assume that IL is on his back side, since we need to get through that in order to get him to zero.
So, on most turns, IL will deal 3 instances of damage each turn (more if you play keep moving), for (on average) 2(+4), 2(+4), and 2.5(+4) damage. It will be less until IL gets fully setup with all his ongoings, but if you don't win fast enough, that will be the end result. 6.5 + 3x4 = 18.5 damage each turn, which is not remotely survivable.
3 Liquid forms + 2 biometric plasma vats adds two points of damage reduction, and two instances of +3 healing each round. That's still not enough, but add one Iron form, and you get -4 damage taken, so total damage is 6.5 - 2x4 = -1.5 damage, or a net positive 1.5 hp per round. That's a good starting point, but requires 4 forms, and AZ's power to lock down the environment to maintain, and leaves you with no way of dealing damage. On average, Former Allies and Iron Justice will have you discarding 0.5 cards a turn. Also, with 2 Biometric Plasma Vats out, IL has -5 damage taken and he heals 8 hp a round (if Scholar is using 2 powers). If we bring out the 2 Irridated Cyclohexane Vats, then that reduces his DR to 3, but it also reduces Scholar's DR and necessitates a second Iron Form.
Now if we wish to deal damage to IL then we need Energy forms. An Energy form will deal IL 4-3= 1 x2 damage each round. 3 Energy forms would therefore deal IL 6 damage each round, for a net gain of 2 HP.
So far, we have Scholar gaining 1.5 hp per round, IL gaining 2 hp per round. This requires 8 forms, which means that Scholar is discarding 8.5 cards each round. This is obviously untenable - even with a double Bring What You Need Scholar can only draw 5 cards regularly (since AZ is needed to lock down the environment. But we haven't looked yet at what cards Scholar can play.
Scholar's most useful cards here are Transmutive Recovery, Proverbs and Axioms, and Expect the Worst. TR nets you 2 cards, 5 hp, and (5-3)*3 damage. Proverbs and Axioms is 1 card, 5 hp, and (5-3)*3 damage. Expect the Worst is 5 hp, (5-3)*3 damage, and removes the 6.5 damage you would take, for a net gain of 6.5+5 = 11.5 HP. If you could play one of those every turn (which I doubt that you can), then you would average +1 card, +7 hp, and 6 damage, for a grand total of -2.5 cards, +8.5 hp, and 4 damage. This is more health and more damage than we need, but not enough cards. If we remove an Iron form and an Energy form, then we net -0.5 cards, +2.5 hp, and +0 damage. Or, since some of IL's healing is tied to Scholar's power use, we can replace the Bring What You Need use that Grampa Legs provides with a simple Draw a Card, and shift that to -1.5 cards, +2.5 hp, and +2 damage. (This is 2 Energy Forms, 3 Liquid Forms, and 1 Iron Form)
I could play with the numbers a bit more, but I don't think that I'm going to do much better than this. When Iron Legacy is fully set up, Scholar simply can't hold enough forms to maintain hp gain and damage dealt. If it comes to a war of attrition, without ongoing destruction the Scholar loses.
But it need not come to attrition. If Scholar were to get multiple energy and liquid forms out in one turn (using Keep Moving) while a combination of Biometric Plasma Vats and Irridated Cyclohexane Vats were in play, then you could probably heal enough to get IL down low enough that a Checimal Explosion would take him out. This requires him not to have much (if any) damage reduction, and using AZ to have him deal himself cold damage will help, but I think that it is doable if you get lucky.