Pretty much any scene where Riggs is pissed off at someone or suicidal. Most Notably:
In the first movie when he breaks free of his Shock Torture, before going after Joshua. Earlier on when Murtaugh didn't take his suicidal tenancies seriously until he almost shot himself.
The second movie when he finds out that not only The Dragon of the group killed his wife, they also killed his current girlfriend. The latter wasn't found out until they tied him up and left him to drown.