For version 2, keep in mind that unlike in 1 and 3, attacking isn't only effective, but your ONLY way of getting past most of the enemies. For every enemy except the Slime Queen, low kicks or jump kicks will be your bread and butter. They have insane reach that goes long past the end of your boot.
Also, some stages have extra lives scattered around if you go the right path. I believe I've found 4 so far, and it makes life a lot easier.
For the Slime Queen, hitting her with the rod is the best option...though I haven't managed to get past her third phase yet to see if there's more.
My personal favorite is the large black slime.