Here is my general rule for 1-player opponents (it doesn't apply to all of them, but it's a decent rule of thumb): if you have standard weapons for your stats, you can usually beat a 1-player opponent who is one or maybe even two strength boosts above you -- so if you have the 35 boost, as you do, you
should be able to beat Meuka, who has the 55 boost (one above you). However, that is assuming you have decent weapons. If all your weapons are in the 6-8-icon range, you should grab a couple 9-iconers like Stone Club and Ice Club (or even the new Tyrannian Lupe Tooth) and then use the strategy I posted earlier in this thread (which I will repost slightly changed below)... or train until your strength is 55.
Weapons:
-Two good attackers (9-iconers are fairly cheap now)
-One freezer
-Leaf Shield
-Purple Sticky Hand
-Downsize!
-A healer
-One-use bomb like ornate fighting fan or chocolate chip battle biscuit to use when he's frozen
1: freezer*, purple sticky hand, burrow
2: two strongest weapons (usually main attacker and bomb), fierce attack
3: two strongest weapons, sink
4: best weapon, (stolen) downsize power plus, fierce attack
5: best weapon, downsize!, species ability
6: best weapon, leaf shield, species ability
repeat #6, or heal if you need to, or whatever.
* Now, round 1 is really going to suck unless you want to shell out for a scroll of freezing, because you're going to have to get lucky and have your freezer freeze AND your purple sticky hand steal at the same time, and that doesn't happen a lot. So expect to have one or both of them miss and have to withdraw and heal quite a few times. Luckily, you can heal just by fighting Inflatable Balthazar, who can't punch back.