Big breaking putts are putts where the ball will experience a large amount of curve on the putting green as it is struck towards the hole.
These putts swing dramatically left to right, or right to left, depending upon the slope that you are facing and what you need to work on with such big breaking putts, is to get the ball to drop into the hole from the high side, as the ball will not roll in from the front, due to the amount of slope.
If you under hit the putt, so that it does not curve the amount that it needs to, the ball will miss the hole on the low side and never have a chance of going in. It is crucial to ensure that you hit the putt high enough up the slope, so that gravity can then pull the ball back down towards the hole and you can watch it roll in as it approaches from the high side.
In order to achieve this, that the ball approaches the hole from the highest side, you need to work out how much curve the putt has and where the maximum extent of this curve will be, that is the point where the ball will begin to move back towards the hole. Once you know where the maximum extent of the curve is positioned, you simply need to aim the putter face at this point, set yourself up to swing the putter towards that point and then work on achieving the correct speed to get the ball to that point, so that once there it then begins to move back towards the hole.
A great drill to work on to help you decide on how much curve there is on the putt is as follows. Go to the putting green where there is a big break, or slope. Imagine what you think the curvature of the putt will look like and then simply roll a golf ball from your hand at the hole and see what happens. Notice how much the ball curved, the shape of the curve, etc. With a second golf ball adjust your initial roll direction so that the shape that you have just seen still happens, but this time finishes in the hole. Do this with the two balls from different positions around the green, just watching the first ball roll directly at the hole and noticing the shape it rolls along, then applying this knowledge to the second ball and working on getting the second ball to finish in the hole.
After doing this drill and improving your green reading skills, you are now ready to work on improving actually hitting the putt. Take a ball and position it on the green so that you are facing a big breaking putt. Decide on the shape of the curve that the ball needs to follow to finish in the hole. Place a tee peg where the maximum extent of that curve is. Work on hitting the ball up to this tee peg so that the ball gets to it and then curves around it to then move back down towards the hole. Aim your putter face at the tee peg, not the hole. Set yourself up to swing the putter at the tee peg, not the hole. Focus on getting the ball to the tee peg, not the hole.
When you play the putt towards the tee peg watch what happens to the ball. Does it actually get to the tee peg before it curves? Does it travel too far past the tee peg and then curve? Work on getting the ball to the tee peg correctly. Once you are doing this, watch how the ball rolls down towards the hole. If it is moving too quickly, the tee peg needs moving out further. If it is moving too slowly and does not reach the hole, the tee peg needs moving towards the hole. If the ball misses on your side of the hole, move the tee peg further away from you and if it misses beyond the hole, pull it closer to you. Once you have adjusted the tee peg position, play the putt again and the ball should finish closer to the hole and eventually in.
Do this drill and work on achieving the correct tee peg position as quickly as possible and as a result of playing the break more correctly and more quickly, you will find that when you are then next out on the golf course, you are able to play big breaking putts much more effectively and as a result take fewer putts, which will lower your score.