What happens if someone Doomblades a creature in response to you trying to give it Indestructible?
Your creature will be destroyed

As you correctly noted, the stack resolves in reverse order of casting, and if your opponent casts Doom Blade while Adamant Will is still on the stack, Doom Blade will indeed resolve first and destroy the creature. When Adamant Will would resolve, it will go to the graveyard without resolving  because it has no more legal targets.