You must earn each of the following stars in the corresponding level to earn its "Ace" achievement. The blue star is unlocked by completing the level. The green star is earned by completing the level under its qualifying time, which is displayed next to the "Q" under your time after a level ends. The yellow star is obtained by completing a level with 100% accuracy.
Easy "Drinker Drinker" achievement
Complete level 4-15 as usual. When you reach the finish pole, jump over the fence behind it and get close to the martini glass. Jump on it to earn the achievement.
Easy "Graves" achievement
At the end of level 2-5, instead of touching the ending pole, move to the edge of the platform to the right. Look down and to the right to find a small island. Drop down to it and move forward to find four brown mounds, which are graves. Get close to them then complete the level.
Easy "Harakiri" achievement
Jump in place and while falling back to the ground repeatedly shoot below you. You will respawn at the starting location with the same effects as if you were hit by an enemy. You must then complete the level.
Easy "True Samurai" achievement
Dodge a bullet by doing a right angle. Look at a bullet and move left or right to form a right angle.
Easy "Ace City", "Ace Forest",...