The difficulty setting only affects how much hits your character can sustain:

• Easy -- 7
  
• Normal -- 4
  
• Hard -- 2

Falling of the cliff or on the spikes will result in death on Normal and Hard difficutly, but on Easy it will count roughly as 1,75 damage point and the character will be returned to the previous position (except Stage 7).

Enemy HP, cakes, drops, firing rate, bosses etc. are not affected by difficulty setting.

There are 6 types of weapons, sorted by rarity:

There's a separate achievement for finishing the game with each character:

Apart from regular completion achievements, there are 6 special achievements for specific stage completion:

The simpliest way to obtain these is to start the game on Easy difficulty, that way you won't die by falling. Au contraire on Normal and Hard difficulty falling off will lead to death right away, which makes getting the achievement MUCH harder.
However, falling in Stage 7 on any difficulty will lead to death, so pay attention, especially in Duck Mode.

The ★-timings are the same for all difficulties, though on Easy you can just pass by enemies which are hard to avoid to save time. I recommend getting these achievements first, because you'd probably get a lot No Damage levels if you do everything right (since receiving damage slows you).
See Appendix A for the list of my ★-qualifying timings (completed on Easy).

These achievements are not so difficulty dependent, and the best deal here is not to rush. If you're attempting this achievement on a fresh save, start on Normal or Hard difficulty, since HP doesn't matter here, but you can easily restart level by falling off (so you'll be less frustrated for not having a restart button). Some levels are much easier if you have specific weapons, for example I don't recommend you having a big gun at all, the best choice would be triple gun or laser gun (rare). You can get the No Damage bonus playing both Clive and Ms. Johnsson.
The Duck Mode achievements is obviously much harder because you can't shoot, and require some advanced dodging techniques and timing.
See Appendix B for a YouTube video of No Damage Clive run.

See Appendix C for boss tips on achievements.

N.B.: both No Damage and ★ achievements must be completed throughout one save slot (each). The bonuses aren't summed up across saves.

The bosses are quite easy as the game itself, but here are some tips if you're attempting achievement runs.

Boss 1
Jump when he aims you, move away when he jumps, duck when he sprays from top to bottom.

Boss 2
Stay near the box and spam triple gun, the top bullet will git the boss. It's quite safe, but will take a lot of time.
Stay on leftmost top box, duck when he hits with his arms. Bombs which fell down will not hit you with fire. Jump down and hide behind boxes on fire spray (it's bugged and sometimes can hit you even there).
For ★-time you should get big gun and just jump and spam fire, hoping to defeat him before fire spray or bomb hit.

Boss 3
Stay very close and spam fire, the hand will not reach you if you're close enough. When he swings, duck directly underneath him.
★-time is quite high here and requires a bit of luck so that the boss don't jump a lot across the room. If he performs his regular gun/hand attack 2-3 times in a row and you just spam him with triple gun you should make it.

Boss 4
You'd probably get both ND/★ in a regular playthrough as this boss is very easy.