At the start of the game you always have 3 water bombs. You can however upgrade the amount you carry by 4, so fully upgraded you will start with 7. I wouldn't worry about trying to get this quickly as you should be making use of the water bombs as you play. Especially on Labs and Factory as they work well on the green flames.
A quick way to unlock this is to load up the tutorial, throw the 10 water bombs you start with, pause and restart. Throw another 10 and repeat until you hit 100. I did a recording of this, but it doesn't show the trophy unlocking although it did: