Here's something I did once I saw I could kill the last boss :

1) Wait for the cooldown if not ready
2) SAVE your game
3) Kill the boss
4) If you didn't get the legendary drop, LOAD your game and go back to step 3
5) If you got the legendary drop, SAVE your game and go back to step 1

It does work and you do get the item eventually (I'm writing this as I just got the last item for the first time).
So, eventually you will get the legendary item maxed.
It's going to be really slow, but way faster than if you waited for the timer to reset for each fight.

Each fight has a cooldown of 1 hour and 30 minutes (for the last boss).
Someone said something similar already, but with a 1% drop rate and 20 items needed to max out the item, you COULD max that item with around 2000 fights, which would mean spending around 3000 hours or 125 days of uninterrupted play, which basically means you won't get the achievement under a whole year or two.

I'm pretty sure you would rather save & load your game than wait for the cooldown each fight, if you're going for the achievement. Especially if it's the last achievement you need.

In case anyone is interested, the item (at lvl 5) gives +11% Damage, Gold, Exp, Health, and Crit DMG. More importantly, it's a Torch, which means it won't take an Accessory slot. It's basically free stats.