There are 2 ways to earn more intros for characters. Either find them in the Krypt or get them as a reward in a character tower in Towers of Time mode. It seems they're very rare to find in the Krypt as I haven't found any there yet. I got 5 in the Towers of Time mode.
Completing a characters tower series of Towers is guaranteed to reward an intro when all are finished. To be clear, I'm referring to the Towers in the upper left.
Highlight this and hit
. Pick whichever character you want. The 1st group from each character always cost 25,000 coins to unlock. When you spend it, hit
to summon the tower. You will need to complete 5 towers to unlock the intro as well as a skin and other rewards. Each individual tower has rewards as well. To start, only one tower with be available. Complete it to unlock the 2nd. One of the 2nd's rewards are 50 souls. The 3rd tower requires that many to unlock it. The 4th tower will require 25 uppercuts to be performed with character. The final tower requires 25 throws to be performed. In these towers, only the character that it revolves around can be used.
These towers can get pretty difficult and very frustrating. The towers are set to medium difficulty and can't be changed. The opposing A.I. can get be cheap. The will be modifiers to help the opposing A.I. in some matches. Fortunately you can have the A.I. fight matches for you. I suggest have the A.I. fight if you have trouble with an opponent. I find the A.I. wins for you more often than not. To have the A.I. fight you must 1st select the character and when the window to select variation appears, there is the option to turn on A.I. with
. Any time in a tower you can pause and chose fighter select. This will take you back to character select screen and you can change to back to or from the A.I. when it suits you. You will return to the same match you were on so no need to worry about losing spot in current tower.
You can use konsumables in each match to help you whether you fight yourself or have the A.I. do it for you. I would recommend using the Philosophers stone if you have one, on tower 4. It doubles all coin rewards for the whole tower. That tower rewards 62,500 coins at completion. That konsumable will double it to 125,000 coins.
Once you unlock a new intro, you need to go to the character kustomization. Select the character and chose any variation. Select intros and you will see all 4 intros for the character. The newly unlocked intro will have an empty box. Click on box to turn on intro and the achievement tracker will move up 20% for each new intro.
You're have to go through this process 5 times unless you're lucky enough to find an intro in the Krypt. The Krypt seems to have a low RNG rate for intros. Towers of Time look to be the surest way to unlock some.
Sorry if this is a bit long-winded. I wanted to be as descriptive as possible. Especially since as I post this guide, I'm showing up as the only person on this site to unlock this achievement.