"尽管极为不利" can be translated into English as "despite being extremely unfavorable" or "even though the situation is highly adverse".
Here are a few example sentences to illustrate its usage:
1、 Despite being extremely unfavorable, the team still managed to win the game.
(尽管极为不利,这支队伍还是赢得了比赛。)
2、 Even though the situation is highly adverse, we must press on with our plans.
(尽管情况极为不利,我们还是必须按计划进行。)