Mastering solely on a single pair of headphones is a high-risk strategy - you absolutely need to hear what the master sounds like through something pumping larger volumes of air (i.e. speakers) in a bigger space (i.e. than your head), even if it's just a Bluetooth speaker or something.
That said, there's a ton of more mundane mastering tasks that I would suggest you can confidently do on a decent pair of studio headphones - click/noise removal, top'n'tailing tracks, fade in/outs, evening/balancing between tracks etc.
It seems there's quite a jump in the headphone market between what one might call everyday studio cans around $2-300 (Beyer DT880 Pro/Sennheiser HD600 etc) and so-called 'reference grade' models costing > $1,000. No-one can honestly say if your masters will be 4x better if you use cans costing 4x more - you'd have to try some pairs out for yourself, bearing in mind some of the more expensive models draw much more current and will require bespoke amplification to sound anything like their best.
Until last week I hadn't bought a new pair of cans for about 25 years but decided to pop for a pair of Beyer DT880 Pro for general mixing and mastering duties and I'm extremely happy with these. I've always liked Beyer for sheer comfort - they just seem to fit my head and ears better than Sennheiser or AKG - and the sound is really good in conjunction with my Amphion One15s (i.e. no nasty shocks or surprises on either). The DT880s are also more accurate and neutral than the (now rather tatty but still working) DT990s I still have, which still sound great but do weird things to the bass.
Last edited by James Lehmann; 2nd June 2018 at 02:38 PM..