do you round it up or do you round it down on odd lvls?
The DC of this save is equal to 10 + 1/2 the alchemist's level + the alchemist's Intelligence modifier.
You always round everything down unless specifically told to do otherwise.
Rounding: Occasionally the rules ask you to round a result or value. Unless otherwise stated, always round down. For example, if you are asked to take half of 7, the result would be 3.