“He succeeded big time.”
→ “That person was a huge success.”
“That movie flopped big time.”
→ “That movie was a complete failure.”
“You helped me big time.” →
“You really helped me a lot.”
In other words, “big time” is an expression that emphasizes strength.
If you want to use it as a stand-alone exclamation like “Daebak”
“Awesome!”, “No way!”, “That’s insane!”
The tone of voice is “He made it big time!” If you do
“That guy hit the jackpot!”