How to tell if mods disable achievements?
Normally you can see that via the checksum, that'S how it works in EU4 and CK2. When you start the game, the launcher says v1.xx in the corner, followed by 4 characters in brackets, this is the checksum. Once you started the game, versionnumber and checksum will be displayed in the main menu as well. If the checksum is the same, achievements should work, if it's not, they don't.
However, as of 1.02 no mods seem to work with achievements, even something as simple as adding a few more flags disabled achievements for me, despite the checksum not changing and no other indication that achievements are obtainable (you can play ironman without obtainable achievements, so that's no indication).
So, if you want to play for achievements, at the moment I would recommend playing without any mods.
Another methodology to double-check (as of Cherry 2.0.1, the checksum seems broken again — it's claiming “fb8b”, the official checksum for the current version, in the corner; but achievements and multiplayer are definitely disabled with a few specific mods I use):
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Open Multiplayer,
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Ensure both ‘Same mod’ and ‘Same version’ are checked,
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If your current build is achievement-compatible, you should se a large number (not just one or two!) of available servers.
A bit of a hack, I know; but the only way I've found trawling through the internet that actually works for me.