have great fun = have a good time,没有任何区别.
B.had great fun.
你的其他选项被排除,与fun,great time 本身没有关系,而与前面的修饰语表达错误有关,修改后,其他3个都可以正确,语义也丝毫不会改变：
A.had great fun ( fun,/u/,get rid of " a" )
C.had a great time ( a great time,/ c/," a" is a must here.)
D.had a lot of fun/ had lots of fun.( we say either " a lot of..." or " lots of...)