After the first credits: keep the completed-story save, check the Challenges list, and spend CP in the Extra Content Shop on The Mercenaries, the figures, the concept art and two bonus weapons.
The first clear opens two things on the main menu: the Challenges list, and the Extra Content Shop under Bonuses. The shop is paid in CP, which Challenges award, not in Lei; what you did in run 1 already counts. Village of Shadows is open now too; it is run 3. Nothing here can be missed and the shop stays open, but do these steps before run 2, which needs the Karambit Knife. CP can't be refunded once spent.
Make the completed-story saveQuest step
Location
After the Credits · Save prompt – After the credits the game offers a completed-story save: accept it and put it in a new slot, so your save from before the last fight stays as it is. If you decline, the prompt comes back only after you load an older save and win the last fight again.
Summary
The save every later run starts from: New Game+ is loaded from it.
Check the Challenges counters (Bookworm, Heretic, Veteran Gunsmith, Artisan)Quest step
Location
Main Menu · Challenges – Open Challenges from the main menu (it is also in the pause menu during the story, from now on). Heretic and Bookworm should already be complete; if one is still short, its row in section 11 covers what to try. Artisan and Veteran Gunsmith stay short for now: their last recipes and parts need New Game+ stock and the shop's weapons, and they are finished at the end of run 3 (section 14).
Extra Content Shop: buy The Mercenaries, figures, concept art, Karambit Knife and WCXQuest step
Location
Main Menu · Bonuses: Extra Content Shop – From the main menu, open Bonuses, then the Extra Content Shop. Buy The Mercenaries (a small sum; section 15), all 76 figures (8,900 CP), all 120 concept art (100 CP each, 12,000 in all), the Karambit Knife (10,000 CP) and the WCX rifle (30,000 CP). The two weapons aren't handed over here: the Duke stocks them in the story from now on, for Lei. If your CP falls short, buy the Karambit Knife first; keep any CP left over for the infinite-ammo bonuses of run 3.
Main Menu · Bonuses: Figures – With all 76 figures bought, open Figures under Bonuses and scroll through the whole list until every new figure has lost its flashing mark. You don't need to open or enlarge any of them; the trophy pops once the last one is marked.
Main Menu · Bonuses: Concept Art – With all 120 pieces bought, open Concept Art under Bonuses and stop on each thumbnail until its mark is gone; full screen isn't needed. If the trophy doesn't pop at the end, going through the whole gallery again, and restarting the game, has fixed it for some.