You can easily change the disposition of your Dream Eaters via petting certain parts of their body.
There are four dispositions available to each Dream Eater, which are colour-coded. Different body parts lead to different dispositions, and must be treated with different types of petting:
Purple: a poorly-received tap Blue: a well-received tap Green: a poorly-received rub Yellow: a well-received rub
You can also feed your Dream Eater these candies:
Confetti candy = Purple Shield cookie = Blue Block-it Chocolate = Green Ice Dream Cone = Yellow
(The colours do not reference a particular style of battle, and simply organise the available dispositions for each Dream Eater.)
A full guide to each Dream Eater is available here: https://www.gamefaqs.com/3ds/997779-kingdom-hearts-3d-dream-drop-distance/faqs/64749