Although you cannot block each enemy attack, you can do this to many of them. Either tap the screen once or repeatedly.
Bosses
Save single-use buffs and debuff items for Bosses.
Extra hits
You can get an extra hit if a gem is tapped as soon as it appears.
Skills
Use the correct skills for the task. If needed, end a turn while you have star points remaining. They may be more useful when used with the points you are rewarded at the start of the next turn. Garnet's Shield Breaker skill will weaken powerful enemies. Steven's Encouragement skill is useful; upgrade it early in the game.
Star Fruits
Star Fruits are common. Use them to make things easier.