Using Amalgamy
Travel to the Order's Island and visit the Amalgamy Lab. You can also visit the Amalgamy tab in the main menu. From there you can perform either Fusion Amalgamy or Reinforcement Amalgamy. When you finish, a box will appear asking to to confirm your amalgamation and will tell you what time the process will be complete.
The Glitch
Save your game and exit the game after you start an amalgamation. From the main screen, change the time (and date, if necessary) to the time that your amalgamation said it would finish. When you re-enter the game, your amalgamation will be complete and you will not have had to wait the entire length of time needed. You may do this as many times as you wish.
More About Fusion
Fusion Amalgamy uses Quartz Stones and can be used to either teach your monsters new abilities or evolve them into new monsters. Quartz Stones may either be bought or found. The options you will have for abilities and evolutions will depend on the type and quantities of Quartz Stones you own.
More About Reinforcement
Reinforcement Amalgamy is useful for increasing your monsters' stats. Any kind of stat can be increased. Reinforcement can even give your monsters experience without actually battling. However, Reinforcement Amalgamy differs from Fusion Amalgamy in that it spends Amalgamy points rather than Quartz Stones. To use this type of Amalgamy, you must speak with either Mikaela or Jerro.