Most people will tell you it is impossible to visit Sintra for half a day. I do agree with them. Although, you can always do some of it in half a day.
Here is the trick. Its about a 40 minute train ride from Rossi train station in Lisboa. Be prepared for long lines to purchased train tickets on the day, most people are queuing for Sintra tickets anyways. The lockers on the station are pretty handy if you want to leave some luggage behind. Pre buying a train ticket is probably gonna save you about an half an hour extra you could spend in Sintra. As you get out at the Sintra train station, take a right. Get in line for the bus 434. Go to the historic centre, get off and take a 15 minute walk to the Quinta da Regaleira. It cost about €6 to enter. This garden is more than worth it to explore for a few hours. There is the initiation well, beautiful caves, some surprise tunnels and everything is so lush and beautiful in this garden. Embrace the very inspirational feeling you get as you explore the little nooks and crannys. Journal or just enjoy this moment in the sun or shade.
When you are done exploring, you can walk back to the historical centre and as you take a stroll back to the station from there, you will pass many land art pieces, artists, buskers. Its a lovely stroll.
The train returns every 30 minutes or so. On the hour and on the half an hour. Just confirm the departure times on arrival.
Whatever you do, DO NOT use the red bus sightseeing option. You stand in line for a long time without getting unto the bus. If you are only there for a half a day. You’ll have a much nicer time taking things easy.
You will also see many paths in the forest. Its really a beautiful area. Obviously worth a few days or weeks of exploring, but well manageable in half a day if you follow my suggestion.