The Story Goes On

Summoning Lord Pecrtron requires you to have three items in your possession at any given time: the Rabbit of Cearbannog (listed as "Pet Bunny" in the item shop during levels), Two Turtle Doves, and Mother Pecr. All three items are random drops that you can either find in the treasure room of a level (the room marked with a yellow diamond on your map) or in an item shop found randomly in some levels.

It's unlikely that you will find all three in a single playthrough. This means that after you find one or two and finish your playthrough, when you're selecting which area to start from for your next playthrough, review the items at the top of the screen to see which ones you'll keep and which you'll lose. Make sure you pick an option where you'll keep the one or two items you've found, and continue on, hoping to find the rest. You may need to repeat this process multiple times to find all three and have them all at once, but your playthroughs get faster and easier as you progress since you'll be getting stronger and stronger. 

Once you collect the third item, explosions will fill the screen and it'll spawn Lord Pecrtron, a really powerful and invincible AI companion that will stay with you and help immensely. That is also when this achievement will unlock.