accomplish
完成,实现(强调成功完成某有难度之事,侧重「把难事做完做好」)
achieve
实现,取得(强调最终结果/成果,侧重「结果层面的达到」,最通用)
Against all odds, the small research team accomplished their mission to map the previously unexplored cave system.
在重重困难下,这支小型研究团队完成了绘制此前未探索的洞穴系统地图的任务。
The country has achieved significant progress in reducing child mortality rates over the past two decades.
该国在过去二十年里在降低儿童死亡率方面取得了显著进展。