A key objective of education is to prepare individuals to be fully-functioning learners. This entails developing the cognitive, metacognitive, motivational, cultural, and emotional competencies. The present study aimed to examine the interrelationships among adaptability, tolerance of ambiguity, cultural intelligence, learning approach, and language achievement as manifestations of the above competencies within a single model. The participants comprised one hundred eighty BA and MA Iranian university students studying English language teaching and translation. The instruments used in this study consisted of the translated versions of four questionnaires: second language tolerance of ambiguity scale, adaptability taken from emotional intelligence inventory, cultural intelligence (CQ) inventory, and the revised study process questionnaire measuring surface and deep learning. The results estimated via structural equation modeling (SEM) revealed that the proposed model containing the variables under study had a good fit with the data. It was found that all the variables except adaptability directly influenced language achievement with deep approach having the highest impact and ambiguity tolerance having the lowest influence. In addition, ambiguity tolerance was a positive and significant predictor of deep approach. CQ was found to be under the influence of both ambiguity tolerance and adaptability. The findings were discussed in the light of the yielded results.