Use High Damage cards along with SOA and Damage Reducers (DR), Aim to win two rounds with high damage cards and defend with SOA and DRs.
Bryan, Isatis / chiro, Brianna / Arnie, Wyre, Milena, Trish, Thormund, Sabia would be a good 25* deck.
If you have a hard time against attack manipulation clans I'd suggest stop using La Junta and switch to a SOB clan such as Nightmare and Piranas on weeks where the attack manipulators go rampant.
If you do want to play La Junta you can try using SOB and SOA cards to counter the abilities and bonuses, using DRs to stop most of the damage against cards you know you can't beat or you need to use a lot of pillz to beat.
Another thing you can do is use La Junta cards with attack manipulation abilities in order to reduce the effect of the attack manipulators you play against.
I like to play my cards to a safe point where it'd take my opponent the same amount of pillz to beat me. For example, Murray (assuming no bonus) 6 pilled against anita 5 pilled. 8*6=48, 7*5=35+12=47. They'd lose by 1 attack unless they pill 6 as well. Nothing's worse than losing a round AND being at a pill disadvantage. Granted it doesn't always work because they have attack manipulation and they CAN overpill comfortably if they want; they have extra attack to use the round after