What do you do? TBH if it is a full blown tantrum there probably isn't much you can do.
DD had her first ever, and probably worst ever, full-blown toddler tantrum on a plane just before her 2nd birthday. It has gone down in family legend.
It wasn't the first time she had been on a plane. When she was 10 months I flew to Sydney with her single-handed (we were joining DH who was working there for a month.) That flight had a huge delay and we ended up arriving 24 hours late, so it should have been a nightmare. However, DD behaved like an angel and was no trouble at all.
Perhaps because of this I was a bit blasé a year later when we planned to fly to Jersey. The flight was only one hour and at a time of day when she normally had a nap so I assumed she would sleep on the flight. No problem. What a naive fool I was. The difference between flying with a baby and a toddler - oh dear.
It might have been OK if it hadn't been the day of Princess Diana's funeral. We boarded the plane on time only to be told that the flight would be delayed by 40 minutes - something to do with limiting air traffic over London during the funeral procession. Well the trouble started as soon as I tried to put the lap strap seat belt around DD, she really didn't want to be still. Then the screaming started. She screamed and screamed and I simply couldn't calm her. It was so bad that in the end the cabin crew asked for the steps to be brought back and I was allowed to take her off the plane back in to a quiet bit of the terminal building where I managed to walk about with her and get her off to sleep.
However, when I got back on the plane with sleeping DD she unfortunately woke up as I was trying to put the lap strap back on her and the screaming started again. It continued most of the way to Jersey and only finally simmered down when she was offered biscuits.
I am sure I was the most hated person on that plane but there was literally nothing I could do at the time. DH and I were both pretty shell shocked. We did fly again while she was small but it was never that bad as we waited until she was turned 3 and old enough to have her own seat. We also made sure of things to entertain her.