I used same parameters for 2 environments, including batch size. Should I incrase batch size for 8 GPUs DDP 8x times? Does this (hopefully always) guarantees similar accuracy with single GPU cases?

If this is per-process batch size, DDP batch size should actually be 1/8 compared to local training, so that DDP and local both collectively process the same number of samples in each iteration.
If this is already global batch size, can you try to increase the batch size for both DDP and local trianing and see how that changes the perf numbers? DDP would run allreduce on model gradients. So if the batch size is too small, the communication overhead can overshadow the speedup from parallelizing computations.