Teen Titans #14 (1968) checks all the boxes.
I read it decades ago, but no earlier than 1972. This is clearly pre-Crisis and was on old style comic paper.
As the comic was first published in 1968, you could very well have read it in 1972 or later (and of course 1968 makes it pre-Crisis). And the comic was indeed on old style paper, see scans below.
In the issue, the devil-like villain had defeated the entire team except Robin.
The villain is Gargoyle, who broadcasts himself on TV to tell the Teen Titans he will come avenge the "unjust" prison sentenced he served because of the actions of a particular Teen Titan (whom everyone believes to be Robin).
They come to face him as a team, and he uses a strange ring to send everyone into limbo, the world he is "king" of. Robin is said to be too noble to fall for that ring trick, escapes (after Gargoyle unleashes puppeted Titans on him and leaves him for dead).
Robin, to win the trust of the villain, had to allow himself to become "evil".
Robin continues to try to fight crime, but without his team, he's not exactly successful (everyone else believes the other three Titans to have died in their fight against teh Gargoyle). Robin then proceeds to meet the Gargoyle in a graveyard, to turn himself over, joining his teammates in Limbo.
The specific story point is that the process caused Robin's face to transform into an uglier/evil reflection of himself. Robin removes his mask and the transformation moves across his face. At one point his face is half his own and half transformed. He seems (obviously in character) resistant to 'give himself over to' becoming dark.
Gargoyle wants Robin to remove his mask so that he can face limbo as "himself" and not a "miserable masquerade". Robin has a hard time taking the mask off (secret identity and all that), but he yields when Gargoyles threats him with using the former Titans against him once again.
At this point half of his face looks evil/distorted, while the narration underlines how Robin is struggling with himself. Eventually he ends up completely "evil-looking".
The villain, confident in his victory, is undone when Robin says it was an act to fool the antagonist. Robin was able to do this thanks to the fact that Batman had taught him to be a strong actor.
As it happened. Robin enters limbo and immediately proceeds to torpedo his puppeted teammates. Gargoyle is distraughted by these actions, realizing Robin somehow tricked his way into entering limbo without becoming Gargoyle's servant in the process.
Robin explains that Batman taught him "how to be a totally convincing actor" and that he faked having his thoughts filled with evil (through the above facial acting) while he was keeping his mind pure good - by focusing on "how great Gargoyle would look like behind bars!"