Let's see. I'm going to guess legitimately means no Fortify Restoration Potion Looping... My max was probably 259 with a Bound Bow (While bashing). I simply used the Bashing Perks, Fortify Marksman Potions and Marked for Death (single use, full time duration).
Seems pretty legit to me, though defining legitimate is quite difficult
Let's get technical, technical. I wanna get technical ...
For the purposes of "legitimacy", let's assume you mean no necromage/vampirism, no armor stacking, and no potion looping. Pretty much anything else should be fair game, yeah? I'm also going to disregard Marked for Death, purely because if you had enough patience, you could just keep repeating it for hours and then do a single attack that does 100,000+ damage....
Physical Damage:
Poisons active:
Enchantments:
Play on Novice difficulty for the extra damage, if you want to be technical.... Unless I'm forgetting any other abilities, tricks, etc., this should be the setup that yields the maximum damage you can get.
I don't know the exact amount of damage you'd get, all told, but I'd guess it's around 15,000+ if you've done it all properly. Maybe over 20,000 even.
With all your perks mentioned and an extra set without any other boosts from alchemy or enchanted armor or jewlery
Name: Chaotic Hammer
Damage: 125
Warhammer: The Longhammer
Enchantment: Over 300 Chaos Damage, Over 101 Fire Damage and Soul Trap for 2 seconds
Destruction: Augmented Fire, Frost AND Shock 2/2
This all adds up to around 526 per swing with a 30% sing speed boost on top of that.
Berserk Rage from an Orc (The race I use most) Makes it 631 Damage per swing.