For multiplayer, have all four players play as Sweet Breaker and bring as many pudding cards as possible. Selecting the field effects Charity and/or Miracle can also help with getting pudding cards and hypers.
The requirements for this achievement were changed in Version 1.13.1. The change allowed for discarding three pudding cards in a single match instead of six pudding cards, decreasing the requirements for players who had not previously completed them. (The change was made alongside a balance change to Melting Memories that reduced the amount of cards discarded by the hyper's effect.)