Last month three pet cats were also shot in Napier - one died, another lost a leg and the third was still missing after recovering from a shot to the face last August.
Mr O'Sullivan said the shooting had devastated him and his partner, Rachel Campbell, and raised concerns for the safety of their young daughter.
"We are really, really, upset about it, we just feel sick and for us he was more than just a cat, he was our buddy," he said.
"I don't know if there is a link to the other shootings but he's clearly been shot by someone in the weekend and the bullet has penetrated right through his chest."
Vet Services Hawke's Bay confirmed Ralph died from the gunshot wound.
"I have done a lot of rabbit shooting and to me it looks like a bigger calibre gun," Mr O'Sullivan said.
"Rach and I are really upset, especially in the manner it was done, I could accept it if it was an accident but when it is done maliciously it leaves us really concerned about our safety here."
The family lived at the end of a remote road with access only to their property and a rarely-used entry to another farm.
"We have a little baby who is only six months old, so we do have genuine concerns for what else could happen up here."
Mr O'Sullivan has added another $500 to the reward for information leading to prosecution of the culprits. Earlier this week an anonymous Hawke's Bay resident offered $1000 for the cause, and another resident has since added a further $250.
Information for the police or SPCA that may identify the culprits can be supplied to Hawke's Bay Today by phoning (06) 873 0810 or emailing news@hbtoday.co.nz
Recent cat shootings
Havelock North: Last week Animal Care performed surgery to remove pellets lodged in the bodies of two cats.
Napier: Last week Napier SPCA removed a pellet lodged in a cat's mouth after it was shot between the eyes; reports of dogs being fired at in Tamatea. Last month three cats from different Georges Drive properties were shot - one fatally, one needed amputation and one disappeared
Waipukurau: Last week a pellet was removed from the face of a shot cat. This week, the body of a cat was found with a gunshot wound from a high-powered rifle through its chest.