Nicalis announced that online multiplayer will be exclusive for the Wii U version of the game 1001 Spikes. That means the 3DS version of the game will only have offline gameplay. You can read the contents of the tweet below:
@iEfrenR Wii U is the one to get if you plan to do multiplayer. PS Vita and 3DS will not have multiplayer
— Nicalis, Inc. (@nicalis) May 30, 2014