tiger by the tail, to have a

have a tiger by the tail

 and have got a tiger by the tail; have a bear by the tail
Fig. to have become associated with something powerful and potentially dangerous; to have a very difficult problem to solve. You have a tiger by the tail. You bit off more than you could chew. You've had a bear by the tail ever since you agreed to finish that big project.
See also: by, have, tail, tiger
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.

have (or catch) a tiger by the tail

= ride a tiger.
A similar difficulty confronts those who have a wolf by the ears (see wolf).
1979 Peter Driscoll Pangolin You're taking on an organization with reserves you know nothing about. How do you know you won't be catching a tiger by the tail?
See also: by, have, tail, tiger
Farlex Partner Idioms Dictionary

have a tiger by the tail

tv. to have become associated with something powerful and potentially dangerous. (Have got can replace have.) You have a tiger by the tail. You bit off more than you could chew.
See also: by, have, tail, tiger
McGraw-Hill's Dictionary of American Slang and Colloquial Expressions

tiger by the tail, to have a

To take on something that turns out to be too formidable or difficult. This term, with its vivid image of manually catching a wild beast that rewards one with violent thrashing about (or worse), replaced the earlier catch a Tartar, used from 1663 to the late nineteenth century. Emma Lathen wrote, in Murder Without Icing (1972), “The Sloan Guaranty Trust . . . might well have a tiger by the tail,” alluding to an impossible investment.
See also: by, have, tiger
The Dictionary of Clichés by Christine Ammer
See also:
  • on (one's) tail
  • on somebody's tail
  • on someone’s tail
  • on tail
  • on your tail
  • sit on (one's) tail
  • sit on someone's tail
  • turn tail
  • turn tail, to
  • Go chase your tail!