You can activate “Dramatic Rescue” when an Amazoness on your side of the field is targeted, such as with any Equip Spell Card, “Tribute to the Doomed”, “Trap Hole”, “Man-Eater Bug”, “Relinquished”, “Dark Cat with White Tail”, “Amazoness Spellcaster”, “Penguin Soldier” (even if it targets 2 monsters), “Change of Heart”, “Ring of Destruction”, “XYZ Dragon Cannon”, etc. But not when cards like “Raigeki”, “Dark Hole”, “Mirror Force”, “Fissure”, “Creature Swap”, “Guardian Sphinx”, “Bottomless Trap Hole”, “Adhesive Trap Hole”, etc. are used.
You cannot activate “Dramatic Rescue” when your face-down Amazoness is targeted (with “Nobleman of Crossout”, etc.).
You can activate “Dramatic Rescue” when your opponent’s Amazoness controlled by you is targeted; in this case, the Amazoness returns to your opponent’s hand but it is you (the player who activated “Dramatic Rescue”) that gets to Special Summon a monster.
If you activate “Dramatic Rescue” and your opponent chains “Ring of Destruction” and destroys the Amazoness, the Amazoness does not return to your hand and “Dramatic Rescue”’s effect disappears (so no monster is Special Summoned).
If you have no monster to Special Summon, you cannot activate “Dramatic Rescue”.
You cannot Special Summon the Monster Card that you returned to your hand with “Dramatic Rescue”, but if you have a second copy of that monster in your hand you may Special Summon the second copy.
You can Special Summon high-level monsters with “Dramatic Rescue” but not “Special Summon-only” monsters.
If you activate “Amazoness Spellcaster”, and chain “Dramatic Rescue”, “Amazoness Spellcaster”’s effect disappears.
If your opponent activates “Snatch Steal” to take control of your Amazoness, and you chain “Dramatic Rescue”, “Snatch Steal”’s effect disappears.
Netrep Rulings:
“Dramatic Rescue” may not be activated in response to an attack.