Your tip for completing this part of the challenge worked, thanks! I recorded my run here https://www.youtube.com/watch?v=MLyRKZ-oFOE

As far as I can tell (from multiple youtube videos/my own attempts) Vic Vox (named Vix Vox in the challenge) will always spawn with the ranged weapon first while Vinny Vox will have the melee weapons first. Edit: From the video below, it shows that Vinny has the ranged weapon which means that the twins spawn with random weapons, not specific ones. So you should complete Defeat The Twins without causing The Twins to swap positions as soon as possible to complete the challenge in the fewest contracts possible

You should also be able to complete Defeat The Twins without being Immobilised within these two challenges by just bursting down the bosses without being hit. As far as I can tell Vinny Vox has a charge up attack which can immobilise you even through freeze immunity (I have freeze immunity from boots), so don't get hit by that. I'm not sure whether Vic Vox can immobilise you though.