To unlock the Hard difficulty for an activity, earn the highest rank for that activity. Core activities require an "Advanced" rank of 80%. Sports activities require a "Pro" rank of 90%. Alternately, unlock the Hard difficulties by collecting 15 Stamps.
Here's a good way (albeit cheap) to unlock more activities in a single day instead of waiting for them to unlock over time. Simply turn the game on, do a given activity, shut the game off, remove the game from the DS, then put the date up one day. Put the game back in the DS, unlock and play the next activity, and repeat the process as needed.