First Approach:
Switch in on Latios, preferably as it attacks off the bat or before it uses the first Calm Mind or latest before it reaches +2. Proceed to engage in Calm Minds. Since Arceus is faster than Latios, it will be able to be at a relative +1 over Latios, unless Latios also uses Calm Mind in the same turn, until +6 is reached. Suppose then, in our exammple, Latios is at +2 and Arceus is at +3. Judgment, if used then, does 41.7 - 49% to Latios. If Latios uses Roost in the next turn, to try and heal back, it is to no avail, since Arceus can continue spamming Judgment. If Latios uses another Calm Mind, both will be at +3, and so Judgment will do 33.1 - 39%. The next turn, Arceus is still faster, and will be able to do another +3 vs +3 Judgment, which at this point will KO Latios.
Note: This will work best if, in a hypothetical situation, the following conditions are met:
- Arceus switches in on a Draco Meteor, or to a lesser extent on a Psyshock, or as Latios uses the first Calm mind but before it gets to its second.
- Arceus must have a speed-boosting nature with a minimum of 176 EVs in speed to outpace all Latios.
- Latios has switched into Stealth Rock at least once and preferably twice for best results.
- Latios is not allowed to reach +6 in the Calm Mind wars. This can be prevented by attacking when at the beginning of a turn, in a worst-case scenario, both Arceus and Latios are at the same level of boosts (+3 in our example). Then, Judgment will do ~35%, and if Latios uses another Calm Mind, Judgment will still do ~31% in the next turn. If in that turn Latios again uses Calm Mind (being at +5 in our example) Judgment would still do ~27% in the next turn. If, however, it uses Roost while at +4 (and by then having lost ~66% of its health), It will be at ~80% health, following which Judgment would bring it down to ~49% again, and in the next turn, down to 18%. In both cases, the above strategy can bring Latios down to a minimum of 9-18% of its health before it has a chance to Roost a second time and/or get to +6. (If either of these happen, it wins all the time). This is not factoring in a crit (which by this time is more than likely) and assumes that Latios is at full health. In a real case, it is highly probably that Latios is not at 100% health, and therefore can be disposed of by the above method, since it is forced to either be at a relative +1 or to waste a turn on Roost, whereas Arceus Steel will not be OHKOed by Psyshock in any condition should Latios choose to attack
Naturally, this approach might be difficult to wrap one's head around in theory, but in practice, as long as Latios has taken slight hazard/prior damage (usually it doesn't want to waste a turn on Roost if it is at ~80% health simply to get to 100%) Arceus-Steel can beat it down with Judgment even as Latios boosts or attacks. At worst, this makes me reclassify Arceus-Steel as a check and not a 110% counter, but the right timing and strategic play would be able to win. Still, I have edited my earlier post to make this reclassification.
Second Approach:
Use Roar.