Brachiation is a whole body event. From the fingers right down to the feet. Any inactive muscles (by active I mean switched on, not tense, but actively supporting the body as opposed to being in a relaxed state resulting in floppiness) will make brachiation more difficult.
Often people who are struggling to brachiate have forgotten to involve the core and posterior muscles.
The lats should be firmly braced to support the shoulders. Avoid allowing yourself to sink out of your shoulder joint, you want a nice long neck, if you feel your shoulders up around your ears you need to pull up and support more.
Legs that are too floppy will swing ineffectively and create a pulling effect in directions against the motion of travel. This wastes energy and also increases the required energy for each transition.
If the core (mainly abdominal) muscles are inactive the back is likely to become loose, even arch. making activating your lats almost impossible and causing the legs to hang backwards creating a backwards pull when you want to go forwards.
The longer you hang on each bar the more difficult the transition to the next. Think of riding a bike on a steep hill that goes down and then dips back up. If you start at the top and build up speed as you dip up you have enough energy and momentum to move easily up the hill with only a slight gear change. However, should you stop at the bottom and start again you would have immense trouble, require far more energy and need to start down in the low gears. Think of what effect that has on the workload of your legs and the type of muscle movement it creates, often jerking and explosive not smooth and fluid.
Feel the speed of your swing and match your arms to compliment the motion.
Hope that helps. If you are able to describe any particular feelings within your body during brachiation I may be able to give you a more specific and helpful answer.