go to any lengths:
to be willing to do anything, even if it is cruel, dishonest, or illegal, in order to get what you want
Example: He's prepared to go to any lengths to find the men who killed his daughter.
be hellbent on:
informal to be extremely determined to do something, especially something dangerous or something that may have a bad result.
Example: Bob's hellbent on going through with the plan, even though it's sure to end in disaster.
come hell or high water:
use this to emphasize that you are determined to do something in spite of any problems or difficulties.
Example: I'll be there in time. Don't worry. Come hell or high water.