I've said this before on other threads.
A mondo can go through with ryanair as regular hold luggage. All you have to do is take it to outsize baggage after checking it in. You obviously have to pay the extra for hold-luggage, but that's it. We took ours with ryanair from prestwick to milan and back no bother.
Having said that, we flew out to CDG and back this year with air-france and were informed when checking in for the return leg, that Airfrance are meant to charge approx 200euros for items of outsize baggage (don't know if this is down to the baggage handlers or what, but at CDG they didn't have an outsize baggage bit and someone would have to come and manually collect the bag from the check-in desk). Thankfully they didn't charge us anything. We checked their website when we got home and found no reference made of this charge anywhere
Most bouldering mats look like weird big rucksacks, so treat it like that. It is after all, just a bag filled with foam.