This enemy has long range, high health and low damage. Its main power is the ability to permanently freeze cats, or at least until they are knocked back. Henry's area of effect is massive, so no cats are safe from it. However, it does have a minimum range, so if you can get your cats in a good position, you've basically already won. Another strategy is to lure him to your base, as not as many cats will be frozen, and the damage he will do to your base is negligible.
Units that are immune to freeze are great against Henry. Use them even if you may not normally.