You don’t need to solder every link, I usually only solder the end
However it is important that the links are sawn precisely so they
join neatly, and you should use hard drawn un annealed wire to make
the jump rings so there is sufficient tension in each link. This
will keep the chain tight even when the links are not soldered. I
havent known one to come apart yet.
Barrelling the chain once it is finished in burnishing shot will
also work harden the links while it burnishes the chain.