Difficult problem (4)
(Other definitions for crux that I've seen before include "Essence or gist" , "brain-teaser!" , "Decisive point of an issue" , "Core" , "Point of difficulty" .)
(Other definitions for bear that I've seen before include "Heavy carnivorous quadruped" , "Large carnivore" , "stand" , "someone being ill-mannered" , "Pessimistic investor" .)
'difficult problem' is the definition.
(tickler can mean something puzzling)
This is the entire clue.
(Other definitions for tickler that I've seen before include "trout farm employee?" , "Poser" , "One catching trout by hand" , "Difficult problem" , "Poker" .)
(Other definitions for dilemma that I've seen before include "Problem (with horns?)" , "a problem for Shaw's doctor" , "Predicament" , "Difficult problem" , "23 [SPOT]" .)
'difficult problem' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for toughie that I've seen before include "It may prove impossible" , "Difficult problem" , "poser" , "A difficult test" , "DT's new difficult crossword" .)