Are tactics all you need to improve?

As a player rated around 1250-1300, do I need to do anything more than study tactics 1 hour a day and also play a few 30 min games a day if I want to improve as fast as possible?

What is your goal, if you want to get to an ELO of 1400, half hour a day might do it. But chess demands more than that if you have higher aspirations. Practice is the biggest contributor to good chess.

You will improve doing that. Improve as fast as possible? Probably not.

Go over the games you lost or made blunders in, and review these games and poor decisions until you understand where you went wrong. I often get an engine to review my winning games as well as there will always be things I miss whatever the outcome. Still learning, still making blunders and still enjoying the game :)

= go over all of your games.

Point well taken. I remember once the computer analyzed my game and told me I blundered because I failed to see I had mate in 7. I don't call it a blunder because on my best day I am not going to see a mate in 7 combination. Still, it was interesting to find out it was there.

It is a bit depressing to see you are in completely winning position and computer says that you blundered because you didn't play the move that wins a bit faster. It's useful to correct those as well but I wouldn't focus tactics in games where you have significant advantage and computer says you screwed up.

Just solving tactics isn't everything but it is extremely helpful.

I've noticed my own tactics rating has been getting higher since I started to train my visualization but not so much in my blitz, standard or correspendence rating. I believe it is because of my mind is set different when solving tactics and playing a normal game. In tactic puzzle I know that there is the correct winning move or sequence and I actively try to find it but in normal games I sometimes play on 'autopilot' and don't look for the 'right' winning move unless the position looks like there has to be something outstanding.

Trying to import same kind of mindset to playing as in solving tactics puzzles could prove to be worth something.

That reminds me of a blog a read a few years ago. This idea that you wouldn't have seen it on your best day maybe isn't as true as it seems.

In the blog there were several tactical puzzles from actual played games, one of which really frustrated me. I was quite adamant that there wasn't a mate in three as advertised and when I saw the solution I simply refused to believe that anybody would play it in a game instead of the super obvious mate in four. Very naive of me.

Now I would see that mate in three without any problem, so my point is that a mate in seven that you think you would never see maybe wasn't all that obscure.

Perhaps, I would only point out that if we have to consider the moves of 4-6 pieces in the problem, the number of options in a 3 moves mate could be ~100 while for a 7 move mate could be ~20,000-40,000.

At that point it takes a very highly trained eye to recognize a pattern. Especially in a live game of chess where other stressors will be occurring.

Tactic training will improve your game but it won't be the fastest path to improving. The fastest path to improving is working on your weakest link in your game chain until it's no longer the weakest link. The find the next weakest link. Sometimes you need help discovering your weakest links, but you can usually tell what they are. Improving it can at times be more difficult however.

That is true but "Tactic training will improve your game but it won't be the fastest path to improving" is not.  Most if not all beginners weakest link is there tactics and calculation. 

We all can improve our tactics and for many players it can be one of it not our weakest link. But a 1250-1300 player may actually have reasonable tactical abilities for their rating but suffer from failing to convert winning endgame positions or drawing equal ones, some might get bad positions out of the opening leaving them fighting an uphill battle in the middle game constantly, others might have a king attack mentality that causes them to miss better plans- my point is that just because you are a lower rated player doesn't automatically mean tactics are your weakest link and therefore the fastest path to improvement. It can be, but not always. I think tactical training is the simplest to identify and work on to improve, and for many the most fun, and that's why many do it. Nothing wrong with it, but it's not necessarily going to improve your game the fastest.

Oh sure.  I thought you were speaking in general but I realise now you were talking to the OP.

Improve to what?  Over what time frame?

Tactics are the best place to start, particularly checkmate patterns and techniques, but building an opening repertoire (or improving it) is also a must.