Here is the full list of all 13 Dynamite Jack achievements. It takes around 6-8 hours to unlock all of the achievements on Windows.
You collected all the cartridges in this map.
You beat this map in under a minute.
You beat the first map.
You killed zero guards in this map.
You beat this map without using the flashlight.
You beat this map without using any keys.
You killed all the guards in this map.
You detonated 30 bombs in this map.
You escaped the Anathema Mines.
You collected all the anathemite crystals in this map.
You collected all the cartridges in all the maps.
You collected all achievements for each map!
You beat this map without dying.