I can't physically link tiles as that requires a visual interface. However, I can describe a strategy for achieving a high number in a Twenty Link number link puzzle. The key is to plan ahead and prioritize linking larger numbers first.

Strategy for High Score in Twenty Link:

1. Prioritize Larger Numbers: Focus on connecting the highest-value numbers available first. These create longer chains and contribute significantly to your score.

2. Look for Chains: Scan the board for opportunities to create long chains of the same number. Don't just settle for connecting two tiles if you can extend the chain further.

3. Strategic Blocking: Sometimes, blocking off smaller numbers temporarily can create more opportunities for linking larger numbers later. This is a more advanced strategy.

4. Avoid Dead Ends: Be mindful of creating chains that leave isolated tiles. Try to connect tiles in a way that allows for future connections.

5. Consider the Entire Board: Don't just focus on immediate connections. Think about how your current move might affect future possibilities.

6. Iterative Approach: It's often helpful to try different connection paths mentally before making a final move. This helps avoid making irreversible mistakes.

Since I can't see the specific tile arrangement of your puzzle, I can't give you a precise solution. The maximum achievable number will depend entirely on the initial tile layout. Applying the strategy above should help you reach a high score.