Deadly Pair - Clear the game with Lady and Trish
Lady and Trish will be in the same campaign together, just like Nero and Dante.
Since it is the most easiest to S Rank all modes with Nero and Dante, I suggest that you complete the game with these two on Heaven or Hell Mode. Maybe combine the completion of that mode with this achievement.
Make sure you buy all their power-ups if you plan to finish the Bloody Palace with them. I'd suggest spamming with the pistols you have as Lady and do the same with Trish.
Just a quick note, there are 2 cutscenes exclusive to these two's campaign, one is found as soon as you start it and the other is when you beat the last mission.