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"These monsters" means all of your opponent's face-up monsters on the field at the time "Amazoness Archers" resolves, not just the monsters that were flipped by "Amazoness Archers"' effect.
You can activate this card when your opponent declares an attack and if there is a monster(s) on your side of the field that includes Amazoness in its card name, or is named Amazon Archer. All monsters on your opponent's side of the field are changed to face-up Attack Position (Flip Effects are not activated), and as long as they remain face-up on the field, their ATK(s) are decreased by 500 points. Your opponent must attack with all of his/her monsters.
If you activate "Amazoness Archers" during the Battle Phase and your opponent Special Summons another monster afterwards (such as with "Call of the Haunted", or if "Cyber Jar" is flipped), the newly-Summoned monster is not affected by "Amazoness Archers" and does not suffer the -500 ATK reduction nor does it have to attack.
The -500 ATK applies to each monster as long as that monster remains face-up on the field. You can activate multiple "Amazoness Archers" and the ATK reductions are cumulative (so -1000 ATK with 2 copies).
'These monsters' means all of your opponent's face-up monsters on the field at the time "Amazoness Archers" resolves, not just the monsters that were flipped by the effect of "Amazoness Archers".
"Amazoness Archers" vs. "Cat's Ear Tribe": the ATK is 200.
If "Fushioh Richie" or "Otohime" are flipped face-up by "Amazoness Archers' effect, their effects are activated because their effects are not Flip Effects; their effects begin a new chain that resolves after the current chain.
If a face-down "Jinzo" is flipped by "Amazoness Archers", "Amazoness Archers"' effect is not negated.
The effect of "Amazoness Archers" will make your opponent have to attack with all of his monsters if he has multiple monsters on his side of the field. If "Amazoness Archers" is in effect, and later a replay occurs, your opponent cannot choose not to attack.
If "Fushioh Richie" or "Otohime" are flipped face-up by the effect of "Amazoness Archers", their effects are activated because their effects are not Flip Effects; their effects begin a new chain that resolves after the current chain.
Monsters that have already attacked cannot attack again. If "The Dark Door" is active, your opponent still can only attack with 1 monster. Monsters which cannot attack still cannot attack (Toon Monsters the turn they are Summoned, "Ultimate Obedient Fiend" under the wrong conditions, etc.) If "Diffusion Wave-Motion" is in effect, only the monster affected by "Diffusion Wave-Motion" can attack. The ATK reduction of "Amazoness Archers" is still applied in these cases where monsters cannot attack.
If a face-down "Jinzo" is flipped by "Amazoness Archers", the effect of "Amazoness Archers" is not negated.
If you activate "Amazoness Archers" and chain "Magic Cylinder", "Magic Cylinder" does the full damage before the -500 ATK is applied; your opponent's other monsters must attack normally. If you chain "Amazoness Archers" to "Magic Cylinder", the ATK is reduced first and then "Magic Cylinder" does damage.
If either player chains "Negate Attack" to "Amazoness Archers", the Battle Phase ends because of "Negate Attack"'s effect.
Monsters prevented from attacking may still not attack if under the effect of "Amazoness Archers."
Monsters with effects that activate when flipped face-up that are not Flip Effects activate when flipped face up by "Amazoness Archers."
If either player chains "Negate Attack" to "Amazoness Archers", the Battle Phase ends because of the effect of "Negate Attack".
The activation of "Amazoness Archers" does not trigger a Replay. The 500 ATK point reduction is permanent for as long as the affected monster remains face-up on the field. Monsters that are ineligible to attack may still not attack.
If a Replay occurs after "Amazoness Archers" has been activated, the affected player must still attack with all appropriate monsters.
If "Thousand Eyes Restrict" is face-up on the field when "Amazoness Archers" is activated, only the "Thousand Eyes Restrict" may attack, provided it is the opponent's monster. If "Thousand Eyes Restrict" is destroyed in that attack, then the other appropriate opponent's monsters must attack.