Cat A is refered to in FAR Part 29 (Airline Transport Rotorcraft) and is a set of design and performance standards to assure safety. It involves a set of procedures and the charts to go with them to assure that anywhere along the flight path a prescribed climb capability exists after a critical Decision Point on takeoff, and before a Landing Decision Point on approach. Before the CDP and after the LDP, the procedures describe what the heliport dimensions must be, and what the obstruction clearance capabilities are.
True Cat A is not required in any operations in the US and few in the world, but many Ops requirements call for "Enroute Cat A" which means that they accept the inability to make a successful climb away during the few seconds it takes to get to climb speed on takeoff, but demand that the hours spent in cruise allow single engine cruise capability. Most helicopter airlines in the world operate as Air Taxi (Part 135), not as Airline (Part 127) because the FAA recognizes the economic burden of hard Cat A vice the tiny probability of engine malfunction causing a flight mishap.
The real issue is that Cat A from low speed requires vastly reduced payload for today's helicopters, and much larger engines for helicopters specially designed for it. For example, the S-92 is hard Cat A from hover to hover, the S-61 is not at all like that. The S-92 has two engines at 2500 Hp each, the S-61 has two at 1400 Hp.
Cat A requires clearance of a hypothetical 35 foot barrier, climb rate of at least 100 fpm until Vy, then maintaining at least 150 feet per minute climb 1000 feet above the heliport and anywhere enroute.
The design requirements have lots of stuff about separation of the engines (so one quitting doesn't jeopardize the other), as well as fire zone integrity (so you can have a "High and Mighty" type fire and keep flying.)
Old BCAR had a similar set of requirements called "Group A" which were similar in intent, if not detail.