There are several types of chests in BDM.
It is not clear which chests your question specifically refers to.
Most chests are opened by Pets (x3)
the condition is:
1) you must have Pets active
2) Pets must not be hungry
3) your Pets must be at the "chest" before your opponent's Pets
4) your Pets (at least one) must have "free" energy to pick up the contents of the chest