Most likely you have an ignition misfire. Check ign coils, ign wires, spark plugs etc.
Bad speed sensors can cause the car to hesitate when accelerating at speeds below 20 mph. The blockage of the air filters can also cause the car to hesitate when accelerating at speeds below 20 mph.
gravity
I had this problem until I had the timing corrected. It is a very cheap and easy thing to do but best to get a proper service centre to do it. If the timing is slightly out the car will backfire and be sluggish when going up hills and acelerating.
Sounds like it could be a dirty fuel filter, try taking it off and cleaning it.
The problem is likely an electrical one - check your spark plug leads from the distributor to the plugs.
Mine hesitated going up hills when I bought. Plugs and wires took care of the problem.
You are running out of fuel. As you are going up the hill, the fuel is sloshing around causing sudden fuel starvation to the engine.
Cylinder miss.
You provide limited information but at first glance it sounds like a problem with engine timing (perhaps spark plugs). I would take the car to a mechanic for diagnosis.
it could be your air filter, you might not be pulling enough air into the engine. it usually costs less than 10 to fix
The CV joint being loose is one of the main causes for a car shaking while it is going uphill. However, a faulty AC and faulty engine could also be the problem.
A 93 Town Car can hesitate when you first turn it on in the morning because the air filter is clogged. It can also be caused by bad gas.