Geryon was fine, I went a little cheap and shot him mainly, I'm not going for ranks right now.
Lady wasnt too bad - if she uses Kalina Ann a lot I can usually hit her with Killer Bee before she fires and do big damage with combos, but sometimes she seems to keep zipping up to the ceiling and dropping bombs all the time. I got lucky though and it was pretty easy.
Doppelganger was pretty average, took it slow and steady and eventually he went down sure enough.
M18 was painful, the chessboard killed me first time round. Second time I managed to beat it, and I beat the level by fighting Cerberus, Agni and Rudra, Leviathan's Heart, Gigapeda and the various enemies with the pair of Hell Vanguards.
Now I'm up to M19 (main post will update tomorrow) This is my worst level. It took me quite a few attempts to get past the hourglass part (the DT'd enemies with higher HP really cause me trouble). I attempted Arkham but he destroyed me.
My plan now is to stock up on items and try again. The hourglass will be a pain again though :/
When(/if) I beat Arkham, I condsider the game beaten more or less. Vergil might take one or two attempts but I don't mind him (and I actually enjoy it)
So, depending on Arkham, DMC3 Dante's DMD could be done tomorrow.