1) Fluffy's Wits (Head) - Get the blueprint from smashing up Harold the training dummy in your starter world. Build requirements - 20 cotton cloth, Workbench lvl 1.
2) Fluffy's Strength (Arms) - Get the blueprint from Ancient Worm boss. Build requirements - 20 silk cloth, Workbench lvl 3.
3) Fluffy's Courage (Torso) - Get the blueprint from Dragon Queen boss. Build requirements - 40 linen cloth, Workbench lvl 2.
4) Fluffy's Speed (Legs) - Get the blueprint from Hollow King boss. Build requirements - 40 magic fleece cloth, Workbench lvl 3.
Carrots are available pretty early on in the game, look for the worlds marked with a purple leaf (in my world they were 1-05, 1-06 and 1-08. Make sure to go take some damage, either get hit by an enemy or fall off the world (if you have full health you can't eat the carrot).
NB - the achievement does not work with the rabbit costume equipped in the vanity slots, you have to equip it in the normal equipment slots.