Environmental objects are a range of things really. They can go from signs in the streets of the city to rocks in the desert. These are basically the items in which you break and soul points pour out, and change depending on the terrain of the area. Keep an eye out for things like rocks, pillars, shrines, jugs or anything that looks like you could break it within the battle zone. This trophy will pop upon the 10,000th object being destroyed.
If you're leveling via the Mission 07 method, you'll notice plenty of urns and small shrines throughout the stage that can be broken. If you're planning on fully leveling all of your characters this will simply come naturally along the way if you're taking full advantage of these objects for soul points.
Many of the stages in the halls of Hueco Mundo (Blue colored, very linear) offer plenty of shrines to destroy along the way. If I had to suggest a stage it'd be Mission 03 as it's rather short and if you simply go for breaking the objects and then rushing through it's manageable enough.