This is easier with arcpy. If you dont want an arcpy solution I can delete my answer.
Script will list all feature datasets in database, and for each list all feature classes and then clip with specified clip feature. Outputs will be placed in the same feature dataset and with '_clipped' appended to name.
Make sure you have no feature datasets or feature classes in the database but the ones you want clipped.
import arcpy, os
arcpy.env.addOutputsToMap = False #Remove this line if you want all outputs to be added to the map
database = r'C:\Somedatabase.gdb' #Change
clip_feature = r'C:\Somedatabase.gdb\eraser' #Change
arcpy.env.workspace = database
datasets = arcpy.ListDatasets(feature_type='Feature')
for dataset in datasets:
arcpy.env.workspace = os.path.join(database,dataset)
features = arcpy.ListFeatureClasses()
for feature in features: