What could help give the 'wobbly' status in Pokemon Rumble world?

Any attack that deals damage has a chance of inflicting Wobble status. An enemy Pokemon that gets KO'd while wobbling will always be caught. You can inflict this on bosses too, but only when they close their eyes and "charge up" between two attack phases.

A boss usually has a cyclic attack pattern: 3 primary attacks and 1 secondary attack. At the end of this pattern you should see white smoke coming out from their head. This is the interval you have to hit the boss.

Wobbling is essentially what happens when you critical an enemy. They get a typical anime "daze" effect. Stars pop out of their head and there's a swirl.

There are a few strategies to inflict the Wobble status:

• Increase the chances of making the enemy wobble, like using Pokemon with the trait Gutsy (better + or ++ version) and by maxing out your Wobble tree whenever you can.
• A high wobbling chance move like Frost Breath, Storm Throw and Spacial Rend.
• Teach Focus Energy which increases the critical hit ratio, and therefore the wobbling chance too.
• Attacks that have a high hit ratio but low damage. Fling and Endeavor are good examples. Once wobbling, use a super-effective secondary move to quickly defeat the boss.

I suggest you to use a Gutsy Pokemon with a weak move like Endeavor (which slowly reduces enemy's health and then, when his health is lower than yours, it deals always 1 damage) or Leech Seed (reduces 4-5 HP for few seconds). This grants you a lot of chances for wobble.

Anyway, sometimes you can capture a boss Pokemon without them wobbling at all. If they "sparkle", that's a guaranteed capture regardless of how you KO them.

_{NOTE: Combo should also influence how likely you are to capture a Pokemon, but I have no evidence of this.}

Source: Gamefaqs

Critically Hitting a Pokémon causes it to become 'wobbly' for a short amount of time. Defeating it within this window of 'wobbly-ness' provides a 100% capture rate.

Hope this helped!~

I find if you use lots of moves before the boss does its first attack(basically at the very beginning) and defeat it before it starts missing, it sometimes let's you have it,I got 4 bosses in a row with that strategy.