Welcome to Flyertalk nmnm224, welcome to the BA board in particular. It's always good to see new people here, and looking at your schedule I think you've come to the right place. So please stick around and continue to post.

I can't see your membership year end date, but I'm guessing the above list falls within that period, in which case, if you are not careful, you will miss Bronze by 10 points. However those short trips may sometimes be 20 TP per sector, depending on the ticket, in which case you only need one of those. If you had your time again I would have suggested you consider splitting your Tokyo trip either by going via Qatar with Qatar, or via HKG (often cheaper to do it that way), plus consider booking from the European mainland rather than starting from LHR.

So long as you get Silver before the membership year ends you then get it for the following year too, so that gives you some scope to plan it a bit. In the meantime, the cheapest way to help get you to Silver is to get a Pro Active Upgrade to Dublin in Club Europe, or pay for it as an Airport Upgrade Promotion at the airport. That will get you another 30 TPs for around £70. Alternatively something similar to CW to HND, which would cost a lot more, but may be worth it and will add 70 TPs for each leg upgraded.

But most of all, follow this forum and you'll soon see loads of opportunities for both cutting the cost of travel and improving the quality of it.