Bärenpark is mostly about tactics rather than long term strategy. The two key points are: 1) be efficient filling your park, and 2) pay attention to what your opponents are doing.

Be efficient

Being efficient at filling up your park means things that you may have already realised if you've been playing Bärenpark for a while such as:

a) Never end your turn without a tile in hand that you can place on your next turn.

b) Minimize the number of 1 square holes you end up. Typically if you are forced into taking a 1 square piece to fill a gap, then that means you made a mistake. Review your game and try to play more flexibly

c) Take the best tile you can. While you are allowed to pick up a tile from a lower tier when you cover up an orange excavator or white cement truck, this is always the wrong decision unless the supply has run out. You should plan ahead to ensure that you are able to play maximum value pieces

d) Use the "try mode" to help you work out how you can best fit tiles in your park efficiently.

e) Think carefully about how you place your new park areas. You probably want to cover up either the orange excavator and/or the white cement mixers quickly. Getting early pick of the enclosure tiles means getting more choice of shapes and tiles worth more points. Similarly being able to get more than your share of animal houses can give you a significant advantage over your opponent/s.

f) Try to remain flexible and leave yourself open to multiple options for efficiently filling up your remaining space, when possible.

Beginners quite often overvalue completing park areas for the bear statues points. The difference between a bear statue and the one underneath it is only 1 point (or 2 points in 2p which amounts to a 4p swing because zero-sum). You don't want to ignore this entirely but putting off completing an area for a few turns may allow you to get more points from claiming achievements or getting higher value animal houses (3p diff, 6p swing for 2-player) and enclosures than you would've got from getting an earlier bear statue. The real trick is to know when to do this which leads into point 2...

Pay attention to what your opponents are doing

All the ways to score points in Bärenpark are potentially worth more points the earlier you do them (achievements, bear statues, animal houses & enclosures). But it's just not possible to be quick at all of these at once. Take a quick moment to assess your opponents' boards and the supply. What are your opponents working towards? What tiles in the supply might be gone before your next turn?

No matter what an opponent is focusing on, they will be neglecting something else. Or even better, you may see an opportunity where you can beat them to an achievement they've been working towards and then they'll have to settle for a lower amount of points for it.

Generally the best time to claim any achievement (or bear statue) is the exact turn before your opponent is about to get it. If there's no way your opponents can beat you to the achievement you've been working towards before your next turn, it may be worth doing something else with this turn and claiming the achievement next turn instead. But remember to always be efficient at filling up your park too.