Most achievements are straight forward, so I'll leave their description as they are except those difficult ones. If you follow my guide, you should be to unlock most of them automatically. I'll add some note, clarification, or even a separate guide on how to achieve them.
A18. Crushing Blow
Crush a Ram with a Stomper. I've marked the place where you can do this achievement. Basically, you have to lure the Rammer Beetle to chase you while running under the Stomper, then the Stomper will crash the Beetle who is running behind you.
A28. Flying Fury
Kill 3 enemies without touching the ground. Using Kuro's Feather will not count, double/triple jumps and Bash are allowed.
A30. Airborne
Double Jump 5 times consecutively without touching the ground. The place I highlighted above has two portal where you can free fall indefinitely. So while falling, simply jump and let it fall again. Repeat it 5 times.
A44. Juggle Master
Juggle a rock 5 times without it hitting the ground. Juggle means Bashing the rock without it touching the ground. I've marked the place on the map above, so simply keep Bashing the rock there.
A52. Bash Master
Bash off enemies 10 times in a row without touching the ground. Using Kuro's Feather will not count, double/triple jump are allowed.