"凭他们本身的实力" can be translated into English as "based on their own strength/capabilities" or "relying solely on their own abilities".
Here are a couple of example sentences to illustrate the usage:
1、 They achieved success based on their own strength.
(他们凭自己本身的实力取得了成功。)
2、 The team won the game relying solely on their own abilities.
(这支球队凭自己本身的实力赢得了比赛。)