I read your question as you are not asking about the whole set of verbalized rules, but you need a software to process it instead. Please correct me if I'm wrong.
In most languages, including Ukrainian, hyphenation occurs on the boundaries between syllables. In other words, the problem of syllabification is equivalent to the problem of hyphenation.
Unless you are an avid developer, linguist, and NLP/ML professional, you don't need developing your own tool for doing that. Take an existing one. A bonus feature is that both algorithms and dictionaries evolve, and you sooner or later get free updates.
There are lots of free/open-source hyphenation libraries existing, including those for Mozilla Firefox, OpenOffice, and others. They are pretty much complicated, and it will take a lot of your effort to develop something similar.
One of such tools is Myspell Hyphenator.
Since nobody can know all languages, the hyphenation libraries use their meta-language for dictionary definitions. Other people who are familiar with individual languages, develop the dictionaries.
One of such dictionaries is Великий електронний словник української мови (ВЕСУМ) distributed under the terms of By-NC-SAA 4.0 license.
Here's an example how the dictionary looks like.