[WaterLife]

Plants can tolerate a good amount of ammonia, nitrite and nitrates. Unless your levels are extremely high, I doubt the cycling tank is the problem.

Different plants have different requirements.

Your plants might be dying/melting because they are adjusting to their new environment/tank growing conditions. If it's just a transition phase and your equipment and water parameters are still sufficient, the plants should adapt/settle in and grow again. The plants may be dying due to lower light levels, lower/no co2, not enough ferts, water parameters, etc. Not enough information is given to know for sure. I suspect your set up is not up to par so plants may be dying or adapting to less optimal growth conditions.

List as much info you can about your tank.

How long have the plants been in there?
Whats ferts/nutrients are being dosed and what is your dosing schedule (how often a fert is dosed and how much)?
Light schedule? (on/off hours)
Distance light is from substrate?
How much co2 are you injecting?
pH 1 hour before lights/co2 turn on, and pH 1 hour before light/co2 turn off.
etc etc

 

[WaterLife]

Plenty of people here who have far more knowledge than me on plant growing. If no one comments soon, I would suggest posting another thread with a better title that would draw those knowledgeable people to come give you advice. Maybe a title like "Plant issue. Some growing, some dying", "Need help. Plants dying" or something like that. And post it under the "Fertilizers and Water Parameters" section or "Plants" section.

Be sure to list as much info as you can, such as the questions above (include the answers you already gave), pH, even ammonia, nitrite, nitrate levels, plant condition before you got them and after, maybe even GH and KH if you know those, etc.

Dwarf Baby Tears are a pretty demanding plant, so it's most likely melting/dying because your tank conditions (lighting, nutrients, co2 levels) are not sufficient to grow it.
That large anubias, with the one bad shape leaf, looks like it might have been grown emersed (above water), so it might melt as it transition to submersed growth and will slowly grow new leaves.

Do you have any info on what co2 system you are using?