I actually don't remember if rain dance negates burning field. I just remember I used Fake Out on the Illumise and my Slugma got one shot by the second mon or something. That Masquerain should have a water move.
I set up electric terrain instead with Ampharos. Swoobat was also helpful in that battle.
My team at that time: Swoobat / Ampharos / Hariyama / Slugma / Venusaur and a lvl 16 Lombre for Fake Out.
What I advice:
- Level Ampharos and Growlithe to 35.
- Graveler won't do much since most of her mons are special attackers. Either get sturdy on it or only bring it in on the Anorith so you can smack down that thing. (Only if you know you kill the second mon before it can attack.)
- If I remember correctly, Anorith has a seed. Don't attack it first turn since it works like a free protect turn 1. Give this seed to Growlithe as well so you are guaranteed to set the field on fire.
- Replace Beautifly by a fast flying / fire type. Camerupt also murders half her team but it's slow. Trubbish can also be an option. Level it to 36 to evolve and get it back down to 35. It has toxic spikes for extra damage.)
- Box Torterra for this fight and replace it with a fake out user to stop Illumise. (Meowth, Lombre, Espurr learn it early).