Goto level 1-7. There are six ropes. Swipe across the iPhone with three fingers at once and you should sever five of them for the Achievement. Alternate method: On 1-18, swipe two fingers straight up the sides very quickly. It may take a few tries but you can get the Achievement this way.
Awards and titles
Complete the indicated task to unlock the corresponding award or title.
Bronze Scissors: Collected 50 stars.
Bubble Popper: Pop 50 bubbles.
Cardbord Box Completed: Complete the Carboard Box.
Fabric Box Completed: Complete the Fabric Box.
Foil Box Completed: Complete the Foil Box.
Gift Box Completed: Complete the Gift Box.
Golden Scissors: Collect 300 stars.
Master finger: Cut 5 ropes at once.
Quick Finger: Cut 3 ropes at once.
Rope Cutter: Cut 100 ropes.
Rope Cutter Maniac: Cut 800 ropes.
Silver Scissors: Collect 150 stars.
Spider Buster: Outsmart 40 spiders.
Weight Loser: Lose candy 50 times.
Easter mode
Note: This requires the April 2011 update. At the title screen, tap the candy on a string hanging out of the o in rope. The candy should turn into an Easter egg. Play the game, and the candy will be replaced by the egg and Omnom will wear bunny ears for a second when the candy goes close to him.
Tummy Tester Achievement
For this Achievement you'll need Om Nom to open his mouth 10 times in a row. Select Level 1, Cardboard Box and select level 4 of the Cardboard box. Cut the Top, Left and Bottom rope at the same time, leaving only the right rope. The candy will dangle and Om Nom will open his mouth as it passes by. Alternate technique by Shua: On level 3-9, there are sliders. On the bottom slider, just get close to the Om-Nom then away from it ten times. This is the easiest way to get that Achievement.