NG+ All Monkeys!

Unchanged = from regular All Monkeys route

* = You HAVE to do this level after beating Specter if you're on PAL or NTSC

The routing is pretty fluent. It's your choice if you want to do the revisit right after you do the 1st pass, or leave all 2nd passes after beating specter. (On PAL and NTSC-U, this excludes the 3 levels that have the 3 extra monkeys).
Doing both passes at once requires more menuing.

Up until and including Port Calm is unchanged

Viva Apespania:
Leave the first 3 monkeys for the 2nd visit, catch every monkey otherwise.

Castle Frightmare:
Catch the monkey on top of the door in the 2nd area, middle of lobby, then go left and catch the knight. Follow the level and end at the invisible monkey.
That leaves the 2 grave-monkeys, and the 3 monkeys underneath the giant tombstone for the 2nd visit. (Double catch + robot)

Vita-Z factory:
Grab the secret monkey and leave the monkey in the left closed-off place walking. Get him, blue and robot-barrel on the 2nd visit. Route is unchanged otherwise

Casino City:
Get every monkey but the ones in the bar area. That's 2nd visit.
After the middle monkey, you go to the "end" of the 2 spinning platforms with dancing monkeys and work towards the casino and magic monkey.

Ninja Hideout:
Leave first 2, yellow after gate and black for 2nd visit.

Snowball:
Unchanged

Lookout Valley:
Skip the first monkey, clear the cave, then get the monkey in the rock and clear the area afterwards.
That leaves the first red, island red and the white next to him for the 2nd visit. You can swap island monkey and rock monkey if you prefer.

Blue baboon:
Leave the burrowed monkey and the UFO-cave for 2nd visit.

Enter the Monkey*:
Amount of monkeys: 19 on JP, 20 on PAL/NTSC/JP+DLC, first visit needs 17.

• Pal/NTSC: Catch all monkeys according to the route, so that the final 3 monkeys are (Son)Gok(o)u, the one on that same platform, and the one with the gun.
• JP: Leave 2 monkeys at the plaza while catching all the rest.
• JP+DLC: Leave 3 monkeys on the plaza for the 2nd visit.

Simian Citadel*:
Unchanged
(Catch blue monkey and mermaid monkey on 1st visit in last area)
Alternate strat: Catch the green monkeys so that on the 2nd visit, Tommy is easier to catch. Not the case in any JP.

Panic Pyramid:
Unchanged from All Monkeys/Any%
Fully complete Sphinx, then immediately do last 3 monkeys in the pyramid like in other routes.
On second visit, all you need is the top floor in Pyramid.

Pirate Isle:
Unchanged

Land of the Apes:
Catch all the monkeys in the sub areas (sauna -> ski place), finish the 2nd visit with "overworld"

Lost Valley:
Leave 3 at the beginning, go into waterfall and get all monkeys.

Skyscraper City:
Leave the first area (6) monkeys for the 2nd visit
When entering the last area (with the yellow monkey hanging on a sign), fly up for the "secret" monkey to skip the crane section

Code CHIMP:
Catch all monkeys now, going right-way in.
//Doing the level backwards is faster in NG All Monkeys, because you don't need to end in the boss trigger.

Moon Base*:

• PAL/NTSC: Defeat specter first, come back to clean up level.
• JP: Clean up level first, then beat boss
• JP+DLC: Clean up level first, then beat boss.
  (Untested if that is faster, but feels like it).