Urban search and rescue missions require rapid first response to minimize loss of life and damage. Often, such efforts are assisted by humanitarian robots which need to handle dynamic operational conditions such as uneven and rough terrains, especially during mass casualty incidents like an earthquake. Quadruped robots, owing to their versatile design, have the potential to assist in such scenarios. However, control of quadruped robots in dynamic and rough terrain environments is a challenging problem due to the many degrees of freedom of these robots. Current locomotion controllers for quadrupeds are limited in their ability to produce multiple adaptive gaits, solve tasks in a time and resource-efficient manner, and require tedious training and manual tuning procedures. To address these challenges, we propose MTAC: a multi-gait terrain-adaptive controller, which utilizes a Hierarchical reinforcement learning (HRL) approach while being time and memory-efficient. We show that our proposed method scales well to a diverse range of environments with similar compute times as state-of-the-art methods. Our method showed greater than 75% on most tasks, outperforming previous work on the majority of test cases.