Sure, quite feasible. My only concern is that you are mixing a lot of water and mains electricity. You probably want to have the pumps and mains electronics separated by a few metres (off to one side and well-shielded; see if you an achieve IP67 for all the mains electronics) with just pipes and opto-isolated signals going between the play area and the mains/pumping area.
You should be able to run it all off the one pump and a whole bunch of solenoids. One solenoid per gun, one solenoid per filler, one solenoid to drain each bucket. Or you could use big LED bar-graphs to illustrate fill-progress instead of water, which means you need water only for the guns.
You will also need some means of detecting water hits on targets. I would suggest little lightly-spring-loaded metal plates with microswitches on them. Most watering solenoids are 24VAC and about 100-300mA, so you need a big 24VAC transformer and a relay to supply power for each solenoid; you can probably buy an 8-relay shield ready-made for the arduino. And some zener diodes to catch the switch-off transients from the solenoid coils; put a reverse-series pair of 50V zeners across each solenoid.