Download the latest version of Atmosphere and put it onto your SD card. You may want to delete the old atmosphere folder from your SD card before doing so.
Download these signature patches and put them onto your SD card:
https://github.com/ITotalJustice/patches/releases/latest
Download the 13.1.0 system update and put the folder onto the root of your SD card.
Enter RCM and load Atmosphere using the latest version of fusee.bin. Load Daybreak from the homebrew launcher and install 13.1.0. Choose the exFAT option even if your SD card is FAT32.
As for your RCM loader, that all depends on which you're using. I'd configure it to load Hekate, keep an up-to-date version of Hekate on the SD card that it will auto-load instead without you having to update the RCM loader, and configure Hekate to load fusee.bin from the SD card (which you will keep up-to-date).