How to improve in Blitz

I've played hundreds of games of blitz but I am making no improvement. I figured doing drills, lessons, and puzzles would help, but what I can't replicate how I play in puzzles when I play in an actual game, and my mind pretty much goes blank. Is there any better way to improve? If anything I want to improve in bullet and blitz, so if there are any strategies of tactics specific to those I would love to hear them.

Ironically, I'd say that to improve in fast time controls: you should first improve at slow time controls. Most of the best bullet/blitz players in the chess world are also the best in longer time controls. You will gain speed (important in fast time controls) when you understand the position quicker. Pattern recognition, opening theory, endgame knowledge and a host of other elements of the game will dramatically help your bullet/blitz but those things can only easily be learned through longer time controls. 

In short, paradoxically: learn to understand chess well in longer time controls and then changing into faster chess is merely a process of adapting, rather than starting from scratch.

For blitz. just move your pieces around more quickly than your opponent does (while avoiding checkmate) such that your opponent's clock runs out before yours does.  No other skills necessary....

However, if you are interested in playing better chess, try to play mostly longer time controls, including "daily" chess, so you have time to think about what you should be doing. It makes sense that taking time to think about what you should be doing would promote improvement in your chess skills.

This is not to suggest that you should necessarily play exclusively slow time controls or daily games, but they should be the greater percentage of your games, much more so than speed games (rapid, bullet, blitz, etc.) which do almost nothing to promote an understanding of how to play the game well. 

Here's what IM Jeremy Silman has to say on the topic...
https://www.chess.com/article/view/longer-time-controls-are-more-instructive

And the experience of a FIDE Master...
https://www.chess.com/forum/view/general/how-blitz-and-bullet-rotted-my-brain-don-t-let-it-rot-yours