If you clean those seedlings up and transplant to better containers right away, you can probably save them. Their roots are unhappy, they're too crowded, and they are growing impatient waiting for good light. Get some paper drinking cups so the roots can run deep. Trim back the tops to 4 inches and don't let them get taller until they start bulking up. Onion seedlings are tough.

It looks like you have them in plastic tubs, do they have drainage ? You can dump them out and carefully tease them apart, then pot them up individually or 2 in a 6 pack cell. I use 3" pots and put about 15 seeds in. Then tease them apart at transplanting time and they do fine.

I germinate and start growing onions in the clear "lunch meat tubs". This is how I did it this year, and it worked great.

I drill 6 or 8 holes in the bottom 1/4" or 3/8" in diameter. I line the bottom with a paper towel to keep the soil in. I bottom feed the onions through the holes.

When I water, I put them in a sliced open (long way) 1/2 gal milk container with maybe 1/4" water in the bottom. I only leave them in the water a few seconds, it soaks up fast. Don't over water. After a few week, I add a couple drops of house plant food maybe every other time.

I put duct tape around the outside of the meat tub to block light from the roots. I end up with about 75 onions per lunch meat tub. I planted them into the garden after about 2 months, you could do it sooner if weather permits.

They were outside hardening off well before then. I use an old aquarium on its' side as a mini-cold frame or greenhouse during the day (don't let them over heat!). Oh.. I forgot to tell you about the grow lights...

Everything said by the above members sounds right.
I'll just sum it up and say the soil is likely junk and you are probably not watering enough or giving them good light. Sorry for my blunt-ness.

Growing nice seedlings requires giving the plants what they want and not neglecting them.