Probably run with the same anti-Takumi formula.
Gronnraven+, Triangle Adept, Ignis/Moonbow, Bowbreaker/Blue Tomebreaker and Threaten Res.
Fem-Robin is already Male-Robin's nemesis with Blue Tomebreaker so I would probably stick with Blue Tombreaker just in case you run into any Blue Mages.
I dunno if I'm the only one who feels this way but Blue Mages are soooo much more annoying than Red or Green Mages. You got Linde, Ursula, Reinhardt, and Male-Robin all of which are really good.
With this build your Fem-Robin can easily be the deterrent needed to counter any of these guys as well as other lance units. Effie is pretty popular in the arena and can shut down your team if you aren't prepared.