The various upgrades from the shop make the mini-games much easier, especially the Trainers that grant your duck more speed during his all-important feeding. Put this sporty footwear at the top of your shopping list.
Alternatively, if you have the money to spare you can opt to feed your pet using snacks bought at the shop. Aside from saving you from the tedium of the Feeding Game, some of the foodstuffs can improve your pets happiness, too.
Rather than trying to press each button in sequence in the Exercise Training game, rest your thumbs accross the 1, 2 and 3 keys and just press them all as rapidly as you can. A word of caution though despite this (depressingly) being the only effective tactic, theres a chance it could lead to broken phones.