I got this achievement on Level 2-5. You start off with a Bomb Shot, so if you don't want to use mulligans, you can always restart the level by holding your right arm out like you're going for a high five. Mulligans use the left arm.
Perfect Timing is awarded for blowing up the bomb before it hits anything but while it's beeping. Terrifying is for getting a near miss on a goblin.
When the level starts, you'll see a goblin hanging from a balloon just over the castle walls. Aim just a bit past him left or right and use the gauntlets to move it to one side. I found that so long as I was aiming away from him, I got Terrifying, even if he managed to grab on and give me Yeehaw. At that point, wait for the bomb to start beeping and explode it by spreading your arms up and out. Perfect Timing didn't pop for me the first time, possibly because I exploded as soon as I heard the beep, so you may want to hold off for a moment to make sure you hit something. Worst comes to worst, you can always restart.
Once both medals pop, it took about five seconds for the achievement to pop. If you get it on your first shot, use your second shot to put the bomb into the fire shield directly in front of you; that will give you the Giant Bomb medal for the bonus medals achievement.