Are emotions (good and bad) linked with achievement?

For positive emotions, yes it does. Emotions such as enjoyment, hope, and pride, are associated with both motivation and learning (Pekrun et al., 2011), likely because students experiencing positive emotions are able to focus on learning tasks (Durlak, Weissberg, Dymnicki, Taylor, & Schellinger, 2011; Helmsen, Koglin, & Petermann, 2012). Negative emotions are a bit more complex. For instance, boredom, a sense of hopelessness, and shame -particularly if the shame results from students believing they lack ability- have negative effects on motivation and learning (Linnenbrink, 2007; Pekrun et al., 2011). On the other hand, research suggest that slightly increased levels of anxiety and feelings of guilt -particularly if the guilt results from students believing they didn't try hard enough- can increase persistence on challenging tasks (Tulis & Fulmer, 2013).