None of mine got light burned, although my tomatoes got a bit cold burned when I moved mine outside. I started mine in full shade and then slowly moved them into areas that got more and more direct sun. The weather cooperated, too, starting us out with cloudy days and then progressively brighter days.

Do you have something to shade them outside? I have had best luck slipping them under a deck for a few hours midmorning and back out late afternoon. Any midday shade will usually work.

I don't make any guarantees about this working, but what I do is cut the bottom off a 2L bottle, toss the cap away, and stick the whole thing down over seedlings once I move them outside.

That gives them a little mini-environment that boosts humidity, shields them from high wind, and the fogging of the bottle (from humidity) helps lessen the impact of direct sun.

After a couple days like that I'll pull the bottle off one plant to see how it fares and if it looks good I pull the rest of the bottles off the other plants of that kind.