A: It works
B: It will keep you alive most of the time, i wouldnt recommend you 1v5 but it makes you less of a target and less of the "squishy ap carry" steriotype.
C: Its fun! You don't lose your killing sprees nor get accused of feeding unless you are just a terribly unaware player.

Remember, as a DPS carry, YOU MUST FARM. You need those tasty minions, last hit them, get the gold, get ahead and carry your team. A fed carry is a problem for the other team, a tankyer fed carry like I'm teaching you to build is about three times the problem for them. You are a turrent killing beast, no one will dare one v one you unless they have some serious crowd control/are extremely fed and if they do, they likely will be escaping on few hit points.

Note: Spell order doesn't matter, just start with a point in everything, level ultimate when you can. Use common sense really.

Greater Mark of Attack Speed
Why? Attack speed. This build lacks it. Generally doesnt matter as you are critting them for ridiculas amounts at level 18 anyway. The extra attack speed is nice :) especially early game as combined with MF's passive movement speed it makes her quite good harassment.
Greater Mark of Desolation
Armour pen, enables you to kill most squishys and gives you an edge in lane. I combine these with my attack speed runes as i prefer this, if you'd rather get all armour pen/attack speed go ahead, i wont stop you.

Greater Seal of Scaling Mana Regeneration
Mf relys on her skills also to farm, harass etc. Why not give her some extra mana to allow for more spamming and harassment :).

Greater Glyph of Scaling Magic Resist
Magic resist = <3.
Especially useful if you are in mid with a caster. Gives you a lot of magic resist late game, which WILL keep you alive. Don't dis till you try it.

Greater Quintessence of Health
Gives you HEALTH. Early game this could mean the difference between being and getting first blood. Would you rather have an extra few damage etc and be dead, or have these, get farmed and be alive? Yeah, no prizes for guessing which you'd rather.

Runes take care of defence, as do items, so i put 21 in offense as mf benifits from the offense tree. 9 points in utility give you less death time, more exp and a much loved jungle buff increase.
Make sure to pick the point in improved exhaust, again with the being and getting first blood thing, unless you were against me I'd rather you get first blood so for me, do it ;D.

Start with a Doran's Blade this improves survival, lane sustainability etc. Its good.
If for some reason you have to go back, pick up Boots or another Doran's Blade. Also grab a few potions, and a sight ward or two if you were ganked/have a team incapable of calling MIA. Generally unless you're silanced you should be able to simply flash away and chuck Make it Rain behind you. Use your exhaust if you must, dont leave your summoner spells there looking pretty, USE THEM TO LIVE. xD.

Next get a Sheen or start building it with a Sapphire Crystal. Yes it seems a weird item to build for MF, but with your Double Up you are by far the best harassment your poor lane opponent has seen. If you perfect using Double Up even better! Harass time!

Infinity Edge
You are the dps carry, you need your crits and damage. Unless you are Ezreal, Urgot or Corki its a must have. The damage is good, especially if you rush it, and even better if you have Sheen's effect on along with a critical hit (Ownage).

Berserker's Greaves
Mobility in team fights, your passive allows you to move faster around the map, its kinda like a Mobility Boots these give you essential mobility in fights as well as attack speed. Whats not to love :D. Unless the enemy has a really cc heavy team I would always recommend these. If they're that bad rush your banshees veil ahead of completing your Infinity Edge, works better I reckon.

Frozen Mallet
Now comes the more tanky part of this build. A Frozen Mallet along with your passive speed allows you to chase down just about anyone/thing. And as a nice bonus it has health and more damage to add to your damage pool.

Atma's Impaler
Stacks with your current and the bonus Frozen Mallet hit points. Gives MF a good amount of armour as well. Personally I think this items too overpowered for words on tanky dps champions.

Blood thirster
The lifesteal is amazing, the damage is amazing, the survival is even more amazing. All I have to say.

Banshee's Veil
Well chances are by now the enemy team has surrendered simply because you're too fed and unstoppable. If its not, build this and complete your Sheen into a Trinity Force. More health for the Atma's Impaler YAY!!

Guardian Angel
Brilliant item for late game. Sell the boots and get this, as Strut plus Trinity Force makes for a very quick Miss Fortune. Get this earlier if you feel its necessary.




Note: Buy items situationally. If the opponants team has stupid amounts of cc get banshees faster/first. If they're dps get your atmas first. Use common sense please. Get a Last Whisper if the opponants start stacking armour.

Exhaust: Allows you to disable their carry while you kill them. Also useful for just about anything.
Flash: use this to Strut back to safety smugly as your enemies rage + question why you out run them by miles.

Alternatives are
Ignite - early game kills, good against self healers.
Ghost - for getting away and triggering your passive to out run them I guess. I prefer flash on MF.
Teleport - more mobility I guess. since MF is incredibly fast i find it useless on her however.

Don't get.
Cleanse - you have a banshees veil and a ton of magic resist. Do you really need this? Unless you see an enemy ranked team pulling out about 3-4 cc champions this is unneeded.
Rally - does anyone use it
Clairvoyance - supports should get this, buy a sight ward if you're worried about being ganked.
Heal - heals very little anyway. don't take this >< please. Its a noob spell honestly.
Clarity - that's what your mana per 5 runes are for.
Fortify - you demolish turrents. You don't protect them aswell.

Pros:
Fast
Deals lots of damage

Cons:
Often targeted
People often play her badly.

To sum this up, you are squishy still even with a tanky build. Leave the inciating to the tank, you deal damage and screw carrys + turrents over while still coming out strong after team fights to finish off survivors.

Still got some survival tho :D. For if you have a decent team.