Do I need to replace all my tubes at the same time

It probably depends on which tube has failed in what type of amp. If the tube that's failed is an output tube in a push-pull amp where it's ideally part of a matched pair, then you might want to replace both output tubes with a matched pair for lowest noise.

If it's a preamp tube, or a phase inverter or something, then, no, just replace the failed tube.

in an amp, small signal tubes often last much longer than the power output tubes. If one tube out of a group of power tubes failed early in its expected lifetime, just replace that one.

Replace them all then keep the rest of the good ones for back up.

Hard to say. You didn't mention how old the good ones are.

I do like Polk432's answer.