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Ryul will cast shield on himself a round before they rush in to start combat.

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"Sorry, Ryul, I have no idea what those are. But I hope they don't like cold iron." Cortina casts guidance on herself and then grabs her longspear with both hands.

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Initiative
Ryul: 1d20 + 3 ⇒ (5) + 3 = 8
Paloma: 1d20 + 2 ⇒ (17) + 2 = 19
Paul: 1d20 + 3 ⇒ (11) + 3 = 14
Nal: 1d20 + 3 ⇒ (10) + 3 = 13
Cashel: 1d20 + 2 ⇒ (2) + 2 = 4
Cortina: 1d20 + 4 ⇒ (4) + 4 = 8
Red: 1d20 + 0 ⇒ (15) + 0 = 15
Green: 1d20 + 0 ⇒ (16) + 0 = 16
Looks like the only ones up first are Paloma and Cheeper

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@GM: Cortina has a reach weapon and Combat Reflexes - she can make AoOs even when flat-footed. Should I roll some AoOs?

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Paloma moves out from the stairway and readies an attack for when the creatures draw within range.
Cold Iron Scimitar Ready Attack: 1d20 + 5 ⇒ (14) + 5 = 19 Damage: 1d6 + 3 ⇒ (5) + 3 = 8
Not deploying Cheeper yet so maybe Cortina can get her AoOs.

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The two creatures see you and move forward to engage. Unfortunately they have to double move to do so. Everyone is up. Take AOOs if you have them.

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Ryul activates his wizardly power, channeling a small defensive aura around himself and any nearby allies. He then slips into the room and JUMPS OFF THE EDGE!!!
To float calmly down below, ”I’ll go around and flank, hold them here.”
Protective Ward: As a standard action, you can create a 10-foot-radius field of protective magic centered on you that lasts for a number of rounds equal to your Intelligence modifier. All allies in this area (including you) receive a +1 deflection bonus to their AC.
Move and then Featherfall to avoid fall damage.

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Cortina may indeed take an AOO.
Paloma does hit Red as it approaches but it seems they have damage reduction. ((Red: -3))
Red(ref): 1d20 + 3 ⇒ (15) + 3 = 18
Green(ref): 1d20 + 3 ⇒ (3) + 3 = 6
Green goes prone

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Cortina may indeed take an AOO.
I'm not really sure what would have triggered it. They did not leave a square threatened by Cortina, did they?

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I'm not sure where I am on the map, but Nal definitely wouldn't have stayed behind - this can be seen from my post above.
In the name of the Holy Heavens! Arrgggh! Nal rushes forward, deftly using his small size and maneuvering between enemies and allies with the grace of an enraged honey badger (that is, not too gracefully, but very aggressively). He jumps over the back of one of the monsters and immediately brings down his blade, and his eyes are full of holy fanatical rage!
Acrobatics: 1d20 + 10 ⇒ (18) + 10 = 28 - vs DC 10 (full speed) + it's CMD (hope it's enough)
Greatsword (Rage, Flank): 1d20 + 8 ⇒ (12) + 8 = 201d10 + 5 + 1d6 ⇒ (3) + 5 + (5) = 13 VS RED

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Doesn't Cortina have a reach weapon?

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Yes, Cortina does have a reach weapon. However, only leaving (not entering) a threatened square triggers an AoO. The creatures came from the right side of the map and didn't use any ladders on the left side, right? If yes, then no AoO was triggered. Otherwise (=if they did use the ladders near us), then Cortina gets one AoO each.

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Gotcha
Nal leaps and slashes into the reddish one - nearly taking it out (Red: -8)
Green tries to get up ref: 1d20 + 3 ⇒ (4) + 3 = 7 and falls prone again.
Red attempts to get out of the Grease ref: 1d20 + 3 ⇒ (6) + 3 = 9 but also falls prone.
Everyone is up.

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Ryul rushes down to the far ladders and climbs up five feet. He is mostly oblivious to the action above so doesn’t comment on anything.
Double Move with a little accelerated climb at the end. I am guessing the ladders are DC 0 to climb and doing it accelerated is a DC 5. So with his modifier at +5 I won’t roll. If my guess is wrong, I can roll.

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@phaeton_nz: Due to all rules arguing I kind of missed acting on my turn. *facepalm* Cortina would have attacked red as there would be no cover provided by Paloma.
last round:
cold iron Longspear: 1d20 + 4 ⇒ (14) + 4 = 18 (vs. Red who is not prone at that moment)
cold iron Piercing: 1d8 + 4 ⇒ (3) + 4 = 7
now:
cold iron Longspear: 1d20 + 4 ⇒ (19) + 4 = 23 (vs. prone enemy with soft cover, first target is Red if they are still conscious)
cold iron Piercing: 1d8 + 4 ⇒ (2) + 4 = 6