In regards to
@Theron 's point on accessories, you can only equip one accessory and thus can't equip both the Salamander Defense System and the Shield Aug Bracers. Equip the former if you want extra one-shot damage, the latter if you want extra Shields and Shield Defense, or the Santa Hat if you want extra Health. Other options include:
- Lightning Duster for the +60% electric resistance
- Signet of Bravery for some extra Health (half as much as the Santa Hat), Physique and Aim (5 each)
- Any combat drone other than Bimbo Siegwulfe for consistent extra damage per turn
Outside lust mode, Shizuya's attacks deal mixed kinetic-electric crushing damage, so the best armour for this fight (assuming you're going to be taking Health damage) is probably the Pump-King's Platemail. It has high Defense and Health bonuses, +40% electric resistance and +25% crushing resistance from the Plated flag.
You can still use the Gray Goo Armor if you want (its decent Defense and +25% kinetic resistance will be helpful), but its -25% electric weakness will likely be a liability without equipping the aforementioned Lightning Duster to compensate.
As a level 10 (I assume) Mercenary, you'll already have an innate +15% kinetic resistance.
Note that all of the above resistances/weaknesses apply to Health damage only, and that I'm not experienced in health damage based builds so I can't guarantee that the raw stats I'm working off of will translate to being especially effective in-game.
On the other hand, if you're good at both dishing out and taking tease damage, you could use that instead. With close to maxed-out tease skills and 80% Willpower, I managed to beat her using this strategy, despite a two-level disadvantage, no pheromones and only a handful of Sexiness points (as a result of my shield-based tank build).