To catch Klink or Klang, you just need more moves left onto the stage.
For Klink, the initial board has a chunk blocked off by barriers as the main issue. You can get rid of them using Barrier Bash+, meaning that Reshiram and Skill Swapped Throh are great options to get rid of them. If you don't, using a super effective or neutral Pokemon with Eject+ or Eject++ would also help. For the rest of the team you could pretty much go with anything, but I would recommend a Pyre team with Delphox or Skill Swapped Ho-Oh if you have it.
For Klang, you have a starting board with blocks on the field, with two Klang barried near the top. Bringing a Block Smash+ Pokemon like Talonflame will help you get rid of the blocks, and Barrier Bash+ will help you get rid of the barriers so the Klangs match each other. Pyre team works nicely here.
As for Klinklang, it starts off as a puzzle. Do the following moves:
- B2 -> E3
- D3 -> D2
- C4 -> E3
- C5 -> C4
- E5 -> C3
Where A-F are the columns, and 1-6 are the rows. So D4 is column 4, row 4. That should clear everything and break the blocks, and the skyfall with finish off Klinklang.
This answer doesn't help much in terms of catching because I don't know what you have in terms of supports. But Klinklang should help. If you comment the supports I'll gladly help.
If you have any of the tapping megas (Beedrill, Camerupt, Shiny Rayquaza), they would help greatly here.