You want to use a chi-squared test since your data is all categorical. The Kruskal-Wallis is a nonparametric test similar to ANOVA which requires numerical data (a continuous variable).
Edits here are to address the comment below
Thanks for the link but that document seems to imply the same thing I was suggesting. If the outcome variable was instead categorical with 0%, 25%, 50%, 75%, 100% scores as the five levels, wouldn't this imply an ordering: 0 < 25 < 50 < 75 < 100? Doesn't the same thing apply if we just reduce this to pass or fail as 0 < 100?
To answer this, I will present the following example. Consider three medical treatments (A, B, and C). Each treatment results in a certain amounts of deaths (alive vs dead). The null hypothesis I am concerned with is this: not all treatments have the same effect on death (e.g. Treatment B may have the lowest death rates).
H_0: p_A \neq p_B \neq p_C
In this example, with my outcome variable being
status=dead, I can suggest that
dead (as most people would probably like to live). However, my null hypothesis (and research goals) are not concerned with ranking (e.g.
alive > dead or
alive < dead). Instead, it is concerned with how treatments affects the outcome status (
dead). Thus, the type of test I'd be concerned with is a $\chi^2$-test (see: WHAT STATISTICAL ANALYSIS SHOULD I USE? STATISTICAL ANALYSES USING STATA)
So to answer your question, if your research question is concerned with outcome status (instead of ranking order) then a $\chi^2$-test will be appropriate.