Okie dokie so to achieve this achievement is quite simple, Play through the story its unmissable!
However, depending on what difficulty you are playing on may or may not be a struggle. I would reccomend if you don't have the infinite rocket launcher to stock up on ammo for pistol, grenade launcher, and shotgun. Grenades would be a bonus.
The biggest trick to this fight is that shoot him off the bat with the grenade launcher, acid truely works best on the demon puppy but everything will do the trick when he lays down grab your shotgun or pistol and start shooting.
If you run low on ammo there are several places where you can get ammo for pistol and grenade launcher plus some health.
Remember to keep dodging, seriously get really good at dodging! It will help you later on!
Eventually a cut scene will pop and you will have beaten nemmy in his demon puppy form....walk into the clock tower and another cut scene will play and boom your achievement should pop!