With the advance in genome sequencing technology, the lengths of deoxyribonucleic acid (DNA) sequencing results are rapidly increasing at lower prices than ever. However, the longer lengths come at the cost of a heavy computational burden on aligning them. For example, aligning sequences to a human reference genome can take tens or even hundreds of hours. The current de facto standard approach for alignment is based on the guided dynamic programming method. Although this takes a long time and could potentially benefit from high-throughput graphic processing units (GPUs), the existing GPU-accelerated approaches often compromise the algorithm's structure, due to the GPU-unfriendly nature of the computational pattern. Unfortunately, such compromise in the algorithm is not tolerable in the field, because sequence alignment is a part of complicated bioinformatics analysis pipelines. In such circumstances, we propose AGAThA, an exact and efficient GPU-based acceleration of guided sequence alignment. We diagnose and address the problems of the algorithm being unfriendly to GPUs, which comprises strided/redundant memory accesses and workload imbalances that are difficult to predict. According to the experiments on modern GPUs, AGAThA achieves 18.8× speedup against the CPU-based baseline, 9.6× against the best GPU-based baseline, and 3.6× against GPU-based algorithms with different heuristics.