At the start of the boss fight The Arrival Day Gifts is only "The Box of Nice Things" (The purple box with wings in the picture) It flies around the room and will quickly drop out two Chatterboxes. These teeth will chase you around; you can kill them but The Box will spit out more.
After getting the box's health down a bit (to 3\4's I think), It will spawn one of the other two gifts: The hatchet, aka "Celebratory Chopper", which will follow you around the room and will occasionally charge you, or The hand-like "Congratulator", which will teleport around the room and will ocasionally spit out a ring of 6 projectiles.
"The Box of Nice Things" spawns the next item (either the Celebratory Chopper or the Congratulator, depending on which one it did not spawn the last time) when it gets down to about 1\3rd (I think) health. Also, with each named gift destroyed "The Box of Nice Things" and its chatterboxes start to move faster.
During Hard Mode both of the named presents spawn during each spawn period instead of one or the other. Also, the small presents move faster.
Can't Wait to Open It!
Defeat The Box of Nice Things with four or more presents still alive
The Arrival Day Gifts
- Each student receives a gift from the Administrators on the anniversary of his or her Arrival Day. No two gifts have ever been the same. Some are relatively benign, like the slinking device that could walk itself down a flight of stairs while spewing electric sparks. Others are more dangerous like the mechanical lobster claw that chewed through half a dormitory hall before burrowing into the floor and disappearing. Not all gifts threaten to maul or incinerate their recipients. Some, for instance, are only premonitory. One child received a white feather the day before a hawk dragged him off the terrace.
- Unsurprisingly, many students prefer to hide their unopened gifts in disused closets or slip them down coal chutes. The Administrators frown on this practice, which they consider the 'absolute height of ingratitude,' and punish it severely.