This monster’s effect is multi-trigger, and therefore Spell Speed 2. So it may be used against Quick-Play Spell Cards.
You can Tribute “Maryokutai” to activate its effect during the Battle Phase if it is not attacking or being attacked.
Netrep Rulings:
“Maryokutai” may be Tributed during the Damage Step as long as it is not involved in that battle.
Netrep Q&As:
Q: Can “Maryokutai” be legally activated to counter a card used during the Damage Step to increase or decrease the ATK or DEF of a monster?
A: This is legal during the Damage Step. bishop, 01/08/2004