No on-line study guides for the play "The Strong Breed" by Wole Soyinka can be found. eNotes does not have one posted nor do other sites. However, if what you need to do is conduct a critical analysis of the play and write a critical essay, you actually won't need to consult a study guide. In fact, you can't conduct a critical analysis by consulting or relying on a study guide. The critical analysis must be derived from the text. Below are some tips for conducting a critical analysis.
When conducting a critical analysis, what we are doing is critiquing and evaluating any work, whether it is a book, play, poem, movie, song, painting, etc. When we are critically analyzing literature, such as a play, we literally want to determine the author's main purpose and decide whether or not the author was effectual and whether or not we agree. To determine the author's main purpose, you are looking for the author's overall point or points expressed in the book, which are also called themes. For example, a theme in Romeo and Juliet is the dangers of violent, uncontrolled emotions. An author can have one main theme as well as underlying sub-themes. In your critical analysis, depending on how long your essay should be, you'll probably want to choose one to focus on.
Once you have determined the author's theme, you can then evaluate the author's effectiveness and if you agree. Your critical analysis essay will not just state the author's opinion or points; your thesis will state your own opinion of the work. To figure out if the author was effectual, you'll want to analyze the literature. You can do this by searching for and analyzing different literary devices, such as characterization, setting, tone, voice, figurative language, diction, imagery, and syntax. There are a lot of different literary devices you can search for in a piece, thereby using them to analyze the piece, especially for effectiveness. If you are unfamiliar with literary analysis terms, you'll want to familiarize yourself with them so that you can do this sort of writing. Here is a link to a Literary device dictionary ("Literary Devices"). You can also analyze literature for rhetorical devices. When we analyze for rhetorical device, we are analyzing how effectual the author's language was. Some rhetorical devices overlap with literary devices; just remember that your analysis purpose is different. Here is a link to a list of rhetorical devices ("Communication Studies").
Once you have searched for either literary or rhetorical devices the author uses to fulfill his/her purpose, you will then be in a position to decide if you think the author was effectual, form a thesis, and begin writing.
You may also need to consult published literary criticism in order to write your critical analysis essay. Literary criticism is exactly what you are about to do, only its published by scholars. The advantage of consulting literary criticism is that you can use the scholars' points to help prove your own. However, instructors don't always want you to do this. Sometimes instructors want you to use your own head alone to prove your points. If your instructor wants you to consult literary criticism, he/she will let you know. Literary criticism is difficult to find on-line, but not impossible. If you do need to consult literary criticism, your best bet is to find it in the library, especially a college or university library.