Without water, they go into a dormant state from which they may revive after decades if water is supplied; however the extreme temperature swings on the Moon's surface is likely to do most of them in within the month.
"The average temperature on the Moon (at the equator and mid latitudes) varies from -298 degrees Fahrenheit (-183 degrees Celsius), at night, to 224 degrees Fahrenheit (106 degrees Celsius) during the day."
I should have looked up the specific species of tardigrades and where they crashed to be sure, but it looks like they might be okay with the temperature swings.
Although with water availability, presumably there is some time between the highest and lowest temperatures where the tardigrade could survive and proliferate. Of course, there needs to be some kind of food, as well.
Oh. Carry on then.