try (to make an effort to do or achieve something): I tried to open the door, but it wouldn’t open.
attempt (to make an effort to do or achieve something difficult): They attempt to eradicate poverty in this area.
struggle (to make great efforts to do or achieve something): Women are still struggling for true equality with men.
strive formal (to make great efforts to do something or make something happen): We have to strive for greater efficiency.
seek (to try to achieve or obtain something): We seek perfection in our service.
endeavor formal (to make serious efforts to do something): The government should endeavor to control inflation.
exert yourself (to make great mental or physical efforts to do something): We have to exert ourselves to solve this problem.
have a go informal, spoken (make an effort to do something, especially after others have tried): I can’t fix this computer. – Let me have a go.