I hate double battles. And my Pokemon hate water slides.

I'll send in Baskerville my Houndour(M) and Charizard(M).

Charizard! Start with Sunny Day. Then use Brick Break on Nessie. Finally, hit Lyra with Iron Tail. If they try any status moves like Lovely Kiss or Thunder Wave, then smite the offender(s) with Will-O-Wisp.

Baskerville, use Nasty Plot. Then use Dark Pulse on Lyra, and finish with Solarbeam on Nessie. If Sunny Day didn't work or is replaced by your last action, use Thunder Fang instead.

Move (Baskerville): Nasty Plot, Dark Pulse(L), Solarbeam(N)
Sub: ------------------, -----------------, Thunder Fang(N)

Move (Charizard): Sunny Day, Brick Break(N), Iron Tail(L)
Sub: Will-O-Wisp (in response to status anomalies)