Statues...they are a prize for completeing certain deeds in these Dungeon games. These statues are in the shape of 4 of the 4th Generation Pokémon...Bonsly, Lucario, Mime Jr & Weavile. Getting them is a feat indeed, below will explain how to get them and show exactly what to do

Pokémon	Pic of Obtaining Location
Bonsly The first statue that you are likely to get is the Bonsly Statue, this one is obtained by defeating all 21 Mini-Dungeons at the Makuhita Training Ground
Lucario The next statue is obtained when your Rescue Force rank hits 15,000 or above. This can be obtained by doing a fair few of the hard Missions found at the noticeboard
Mime Jr The next statue is obtained from doing one of 2 rare * Leveled missions in a long 99 floor dungeon. Once you have completed them you will be given the Mime Jr Statue as awarded
Weavile The next statue is obtained from doing one rare * Leveled missions in a long 99 floor dungeon. Once you have completed them you will be given the Weavile Statue as awarded