Face correctly guessed clefairy. Kudos for cecil for correctly interpreting the sixth line.
Houston, Houston, we have a problem. Houston refers to Whitney Houston as well as the moon mission; Whitney owns a clefairy
Communication’s failing. Should I repeat myself? Whitney's clefairy has doubleslap, which is a repeated strike
Please repeat yourself again. As Cloneblazer figured out, this refers to encore, another move of Whitney's clefairy
Did I hear right? I’ll repeat what you said back to you. Refers to mimic, which repeats the opponent's move, another move of Whitney's clefairy
Systems steady. Refers to the fourth move, metronome; a metronome is meant to keep steady time
Do not fear. I am confident that I can do anything. Metronome causes any attack
Nothing stands in our way. The Plain Badge allows obstacles to be moved out of ones' way
Our destination is not new. Because clefairy's from the moon
My companion fully cleared this terrain. The companion is miltank, a reference to the nursery rhyme line, "The cow jumped over the moon"
Worry not, Houston.
I have been here before. Again, because clefairy is from the moon
*returns the Riddle ball to Freaky Face*