Getting through the dice Palace can be tricky if you get sent back to the start (which happens more often that not) each of the item rooms holds one health pickup (the last room has two) and two fights will offer health. The one with "destroy", a timer and the soldier in a ships cockpit shouting "no" is easily missed. There is a health item on the box on the far left.
The phantom also has health (be careful to jump his bombs though) make sure you are close to him when defeated as you'll leave the room before reaching the health if too far away.
The hardest mini boss is probably "Curry and Rice" where you cannot use your weapons. To defeat him move in close and get it to attack, when it performs it's spinning jump attack there is a pause between each phase where you can use your jump attack to hit him and knock it back.
Another tough one has four bouncing balls and a wall that pulses up and down, just keep firing but when the wall closes is slide under it to avoid being hit but the balls and to give yourself space again. Don't try to run or jump under the wall as you'll likely get hit.
The final boss itself is easy enough. The yellow attack you can avoid just by standing in a corner (the lasers don't hit there) the blue attack sends four bombs into the corners so stand in the middle. The red attack will start a fireball nearest where the boss is that move relatively slower across to the other squares, jump over it (the platforms help) to avoid it just. The green attack is similar but moves diagonally to each square, careful placement avoids it.