How do I help the eagle?
Obviously, her chicks need some discipline.
Hit her chicks.
The nymph is afraid of me.
Show her you're not so terrifying.
Give her the flower and say hello.
What should I do with the envelope?
It isn't addressed to you!
Read it anyway!
What should I do at the rainbow?
You can't dig there as it will disappear.
Tell the nymph to WAIT 1, DIG, then go west yourself.
How can I help the dog?
You'll need the eagle's help.
Ask the eagle to get the peg. Follow the dog when it emerges.
I can't find the unicorn.
Play follow-my-leader.
Tell dogs to find unicorn. Tell nymph to follow dogs.
What should I do with the unicorn?
You know the old legend about unicorns?
Give the bridle to the nymph and introduce her to the unicorn.
How do I finally defeat the witch?
First get the unicorn to break the door. 
When the witch arrives, tell the leprechaun to break the wand.